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{{taskCards}} [[Category:Puzzles]] {{omit fromGUISS}}
Set Puzzles are created with a deck of cards from the [[wp:Set (game)Set Game™]]. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck. Each card contains a unique variation of the following four features: ''color, symbol, number and shading''.

there are three colors: ''red, green, purple''

there are three symbols: ''oval, squiggle, diamond''

there is a number of symbols on the card: ''one, two, three''

there are three shadings: ''solid, open, striped''
Three cards form a ''set'' if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: [http://www.setgame.com/set/rules_basic.htm ''basic''] and [http://www.setgame.com/set/rules_advanced.htm ''advanced'']. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
;Task Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
'''DEALT 9 CARDS:'''
:green, one, oval, striped
:green, one, diamond, open
:green, one, diamond, striped
:green, one, diamond, solid
:purple, one, diamond, open
:purple, two, squiggle, open
:purple, three, oval, open
:red, three, oval, open
:red, three, diamond, solid
'''CONTAINING 4 SETS:'''
:green, one, oval, striped
:purple, two, squiggle, open
:red, three, diamond, solid
:green, one, diamond, open
:green, one, diamond, striped
:green, one, diamond, solid
:green, one, diamond, open
:purple, two, squiggle, open
:red, three, oval, open
:purple, one, diamond, open
:purple, two, squiggle, open
:purple, three, oval, open
Ada
We start with the specification of a package "Set_Puzzle.
package Set_Puzzle is
type Three is range 1..3;
type Card is array(1 .. 4) of Three;
type Cards is array(Positive range <>) of Card;
type Set is array(Three) of Positive;
procedure Deal_Cards(Dealt: out Cards);
 ouputs an array with disjoint cards
function To_String(C: Card) return String;
generic
with procedure Do_something(C: Cards; S: Set);
procedure Find_Sets(Given: Cards);
 calls Do_Something once for each set it finds.
end Set_Puzzle;
Now we implement the package "Set_Puzzle".
with Ada.Numerics.Discrete_Random;
package body Set_Puzzle is
package Rand is new Ada.Numerics.Discrete_Random(Three);
R: Rand.Generator;
function Locate(Some: Cards; C: Card) return Natural is
 returns index of card C in Some, or 0 if not found
begin
for I in Some'Range loop
if C = Some(I) then
return I;
end if;
end loop;
return 0;
end Locate;
procedure Deal_Cards(Dealt: out Cards) is
function Random_Card return Card is
(Rand.Random(R), Rand.Random(R), Rand.Random(R), Rand.Random(R));
begin
for I in Dealt'Range loop
 draw a random card until different from all card previously drawn
Dealt(I) := Random_Card;  draw random card
while Locate(Dealt(Dealt'First .. I1), Dealt(I)) /= 0 loop
 Dealt(I) has been drawn before
Dealt(I) := Random_Card;  draw another random card
end loop;
end loop;
end Deal_Cards;
procedure Find_Sets(Given: Cards) is
function To_Set(A, B: Card) return Card is
 returns the unique card C, which would make a set with A and B
C: Card;
begin
for I in 1 .. 4 loop
if A(I) = B(I) then
C(I) := A(I);  all three the same
else
C(I) := 6  A(I)  B(I);  all three different;
end if;
end loop;
return C;
end To_Set;
X: Natural;
begin
for I in Given'Range loop
for J in Given'First .. I1 loop
X := Locate(Given, To_Set(Given(I), Given(J)));
if I < X then  X=0 is no set, 0 < X < I is a duplicate
Do_Something(Given, (J, I, X));
end if;
end loop;
end loop;
end Find_Sets;
function To_String(C: Card) return String is
Col: constant array(Three) of String(1..6)
:= ("Red ", "Green ", "Purple");
Sym: constant array(Three) of String(1..8)
:= ("Oval ", "Squiggle", "Diamond ");
Num: constant array(Three) of String(1..5)
:= ("One ", "Two ", "Three");
Sha: constant array(Three) of String(1..7)
:= ("Solid ", "Open ", "Striped");
begin
return (Col(C(1)) & " " & Sym(C(2)) & " " & Num(C(3)) & " " & Sha(C(4)));
end To_String;
begin
Rand.Reset(R);
end Set_Puzzle;
Finally, we write the main program, using the above package. It reads two parameters from the command line. The first parameter describes the number of cards, the second one the number of sets. Thus, for the basic mode one has to call "puzzle 9 4", for the advanced mode "puzzle 12 6", but the program would support any other combination of parameters just as well.
with Ada.Text_IO, Set_Puzzle, Ada.Command_Line;
procedure Puzzle is
package TIO renames Ada.Text_IO;
Card_Count: Positive := Positive'Value(Ada.Command_Line.Argument(1));
Required_Sets: Positive := Positive'Value(Ada.Command_Line.Argument(2));
Cards: Set_Puzzle.Cards(1 .. Card_Count);
function Cnt_Sets(C: Set_Puzzle.Cards) return Natural is
Cnt: Natural := 0;
procedure Count_Sets(C: Set_Puzzle.Cards; S: Set_Puzzle.Set) is
begin
Cnt := Cnt + 1;
end Count_Sets;
procedure CS is new Set_Puzzle.Find_Sets(Count_Sets);
begin
CS(C);
return Cnt;
end Cnt_Sets;
procedure Print_Sets(C: Set_Puzzle.Cards) is
procedure Print_A_Set(C: Set_Puzzle.Cards; S: Set_Puzzle.Set) is
begin
TIO.Put("(" & Integer'Image(S(1)) & "," & Integer'Image(S(2))
& "," & Integer'Image(S(3)) & " ) ");
end Print_A_Set;
procedure PS is new Set_Puzzle.Find_Sets(Print_A_Set);
begin
PS(C);
TIO.New_Line;
end Print_Sets;
begin
loop  deal random cards
Set_Puzzle.Deal_Cards(Cards);
exit when Cnt_Sets(Cards) = Required_Sets;
end loop;  until number of sets is as required
for I in Cards'Range loop  print the cards
if I < 10 then
TIO.Put(" ");
end if;
TIO.Put_Line(Integer'Image(I) & " " & Set_Puzzle.To_String(Cards(I)));
end loop;
Print_Sets(Cards);  print the sets
end Puzzle;
{{out}}
>./puzzle 9 4
1 Red Diamond One Striped
2 Green Squiggle Two Solid
3 Red Squiggle Three Open
4 Green Squiggle Three Solid
5 Purple Oval Two Open
6 Purple Squiggle One Striped
7 Green Squiggle One Solid
8 Purple Squiggle One Solid
9 Purple Diamond Three Solid
( 2, 3, 6 ) ( 1, 4, 5 ) ( 2, 4, 7 ) ( 5, 6, 9 )
>./puzzle 12 6
1 Purple Diamond One Solid
2 Red Diamond One Striped
3 Red Oval Three Striped
4 Green Oval Two Solid
5 Red Squiggle Three Solid
6 Green Squiggle Two Solid
7 Red Squiggle Three Striped
8 Red Squiggle Three Open
9 Purple Squiggle One Striped
10 Red Diamond Two Solid
11 Red Squiggle One Open
12 Red Oval One Solid
( 1, 4, 5 ) ( 5, 7, 8 ) ( 6, 8, 9 ) ( 3, 10, 11 ) ( 5, 10, 12 ) ( 2, 11, 12 )
AutoHotkey
; Generate deck; card encoding from Perl6
Loop, 81
deck .= ToBase(A_Index1, 3)+1111 ","
deck := RegExReplace(deck, "3", "4")
; Shuffle
deck := shuffle(deck)
msgbox % clipboard := allValidSets(9, 4, deck)
msgbox % clipboard := allValidSets(12, 6, deck)
; Render a hand (or any list) of cards
PrettyHand(hand) {
Color1:="red",Color2:="green",Color4:="purple"
,Symbl1:="oval",Symbl2:="squiggle",Symbl4:="diamond"
,Numbr1:="one",Numbr2:="two",Numbr4:="three"
,Shape1:="solid",Shape2:="open",Shape4:="striped"
Loop, Parse, hand, `,
{
StringSplit, i, A_LoopField
s .= "`t" Color%i1% "`t" Symbl%i2% "`t" Numbr%i3% "`t" Shape%i4% "`n"
}
Return s
}
; Get all unique valid sets of three cards in a hand.
allValidSets(n, m, deck) {
While j != m
{
j := 0
,hand := draw(n, deck)
,s := "Dealt " n " cards:`n" . prettyhand(hand)
StringSplit, set, hand, `,
comb := comb(n,3)
Loop, Parse, comb, `n
{
StringSplit, i, A_LoopField, %A_Space%
If isValidSet(set%i1%, set%i2%, set%i3%)
s .= "`nSet " ++j ":`n" . prettyhand(set%i1% "," set%i2% "," set%i3%)
}
}
Return s
}
; Convert n to arbitrary base using recursion
toBase(n,b) { ; n >= 0, 1 < b < StrLen(t), t = digits
Static t := "0123456789ABCDEF"
Return (n < b ? "" : ToBase(n//b,b)) . SubStr(t,mod(n,b)+1,1)
}
; Knuth shuffle from http://rosettacode.org/wiki/Knuth_Shuffle#AutoHotkey
shuffle(list) { ; shuffle comma separated list, converted to array
StringSplit a, list, `, ; make array (length = a0)
Loop % a01 {
Random i, A_Index, a0 ; swap item 1,2... with a random item to the right of it
t := a%i%, a%i% := a%A_Index%, a%A_Index% := t
}
Loop % a0 ; construct string from sorted array
s .= "," . a%A_Index%
Return SubStr(s,2) ; drop leading comma
}
; Randomly pick a hand of cards from the deck
draw(n, deck) {
Loop, % n
{
Random, i, 1, 81
cards := deck
Loop, Parse, cards, `,
(A_Index = i) ? (hand .= A_LoopField ",") : (cards .= A_LoopField ",")
deck := cards
}
Return SubStr(hand, 1, 1)
}
; Test if a particular group of three cards is a valid set
isValidSet(a, b, c) {
StringSplit, a, a
StringSplit, b, b
StringSplit, c, c
Return !((a1b1c1 ~= "[3,5,6]") + (a2b2c2 ~= "[3,5,6]") + (a3b3c3 ~= "[3,5,6]") + (a4b4c4 ~= "[3,5,6]"))
}
; Get all combinations, from http://rosettacode.org/wiki/Combinations#AutoHotkey
comb(n,t) { ; Generate all n choose t combinations of 1..n, lexicographically
IfLess n,%t%, Return
Loop %t%
c%A_Index% := A_Index
i := t+1, c%i% := n+1
Loop {
Loop %t%
i := t+1A_Index, c .= c%i% " "
c .= "`n" ; combinations in new lines
j := 1, i := 2
Loop
If (c%j%+1 = c%i%)
c%j% := j, ++j, ++i
Else Break
If (j > t)
Return c
c%j% += 1
}
}
{{outSample output}}
Dealt 9 cards:
purple diamond three striped
green diamond two open
green oval one striped
red oval two solid
purple squiggle two striped
red diamond three open
red diamond three open
green oval one solid
red oval two solid
Set 1:
purple squiggle two striped
red oval two solid
green diamond two open
Set 2:
green oval one solid
red diamond three open
purple squiggle two striped
Set 3:
green oval one solid
red diamond three open
purple squiggle two striped
Set 4:
red oval two solid
purple squiggle two striped
green diamond two open
Dealt 12 cards:
purple oval two open
purple diamond three solid
green squiggle three striped
green squiggle one solid
purple squiggle one striped
purple squiggle one solid
green diamond two solid
purple squiggle one striped
red diamond two striped
green diamond one open
green oval one open
red squiggle one open
Set 1:
purple squiggle one striped
purple diamond three solid
purple oval two open
Set 2:
purple squiggle one striped
purple diamond three solid
purple oval two open
Set 3:
green diamond one open
red diamond two striped
purple diamond three solid
Set 4:
green oval one open
green diamond two solid
green squiggle three striped
Set 5:
red squiggle one open
purple squiggle one striped
green squiggle one solid
Set 6:
red squiggle one open
purple squiggle one striped
green squiggle one solid
C
Brute force. Each card is a unique number in the range of [0,81]. Randomly deal a hand of cards until exactly the required number of sets are found.
#include <stdio.h> #include <stdlib.h> char *names[4][3] = { { "red", "green", "purple" }, { "oval", "squiggle", "diamond" }, { "one", "two", "three" }, { "solid", "open", "striped" } }; int set[81][81]; void init_sets(void) { int i, j, t, a, b; for (i = 0; i < 81; i++) { for (j = 0; j < 81; j++) { for (t = 27; t; t /= 3) { a = (i / t) % 3; b = (j / t) % 3; set[i][j] += t * (a == b ? a : 3  a  b); } } } } void deal(int *out, int n) { int i, j, t, c[81]; for (i = 0; i < 81; i++) c[i] = i; for (i = 0; i < n; i++) { j = i + (rand() % (81  i)); t = c[i], c[i] = out[i] = c[j], c[j] = t; } } int get_sets(int *cards, int n, int sets[][3]) { int i, j, k, s = 0; for (i = 0; i < n; i++) { for (j = i + 1; j < n; j++) { for (k = j + 1; k < n; k++) { if (set[cards[i]][cards[j]] == cards[k]) sets[s][0] = i, sets[s][1] = j, sets[s][2] = k, s++; } } } return s; } void show_card(int c) { int i, t; for (i = 0, t = 27; t; i++, t /= 3) printf("%9s", names[i][(c/t)%3]); putchar('\n'); } void deal_sets(int ncard, int nset) { int c[81]; int csets[81][3]; // might not be enough for large ncard int i, j, s; do deal(c, ncard); while ((s = get_sets(c, ncard, csets)) != nset); printf("dealt %d cards\n", ncard); for (i = 0; i < ncard; i++) { printf("%2d:", i); show_card(c[i]); } printf("\nsets:\n"); for (i = 0; i < s; i++) { for (j = 0; j < 3; j++) { printf("%2d:", csets[i][j]); show_card(c[csets[i][j]]); } putchar('\n'); } } int main(void) { init_sets(); deal_sets(9, 4); while (1) deal_sets(12, 6); return 0; }
C++
{{transJava}}
#include <time.h> #include <algorithm> #include <iostream> #include <iomanip> #include <vector> #include <string> enum color { red, green, purple }; enum symbol { oval, squiggle, diamond }; enum number { one, two, three }; enum shading { solid, open, striped }; class card { public: card( color c, symbol s, number n, shading h ) { clr = c; smb = s; nbr = n; shd = h; } color getColor() { return clr; } symbol getSymbol() { return smb; } number getNumber() { return nbr; } shading getShading() { return shd; } std::string toString() { std::string str = "["; str += clr == red ? "red " : clr == green ? "green " : "purple "; str += nbr == one ? "one " : nbr == two ? "two " : "three "; str += smb == oval ? "oval " : smb == squiggle ? "squiggle " : "diamond "; str += shd == solid ? "solid" : shd == open ? "open" : "striped"; return str + "]"; } private: color clr; symbol smb; number nbr; shading shd; }; typedef struct { std::vector<size_t> index; } set; class setPuzzle { public: setPuzzle() { for( size_t c = red; c <= purple; c++ ) { for( size_t s = oval; s <= diamond; s++ ) { for( size_t n = one; n <= three; n++ ) { for( size_t h = solid; h <= striped; h++ ) { card crd( static_cast<color> ( c ), static_cast<symbol> ( s ), static_cast<number> ( n ), static_cast<shading>( h ) ); _cards.push_back( crd ); } } } } } void create( size_t countCards, size_t countSets, std::vector<card>& cards, std::vector<set>& sets ) { while( true ) { sets.clear(); cards.clear(); std::random_shuffle( _cards.begin(), _cards.end() ); for( size_t f = 0; f < countCards; f++ ) { cards.push_back( _cards.at( f ) ); } for( size_t c1 = 0; c1 < cards.size()  2; c1++ ) { for( size_t c2 = c1 + 1; c2 < cards.size()  1; c2++ ) { for( size_t c3 = c2 + 1; c3 < cards.size(); c3++ ) { if( testSet( &cards.at( c1 ), &cards.at( c2 ), &cards.at( c3 ) ) ) { set s; s.index.push_back( c1 ); s.index.push_back( c2 ); s.index.push_back( c3 ); sets.push_back( s ); } } } } if( sets.size() == countSets ) return; } } private: bool testSet( card* c1, card* c2, card* c3 ) { int c = ( c1>getColor() + c2>getColor() + c3>getColor() ) % 3, s = ( c1>getSymbol() + c2>getSymbol() + c3>getSymbol() ) % 3, n = ( c1>getNumber() + c2>getNumber() + c3>getNumber() ) % 3, h = ( c1>getShading() + c2>getShading() + c3>getShading() ) % 3; return !( c + s + n + h ); } std::vector<card> _cards; }; void displayCardsSets( std::vector<card>& cards, std::vector<set>& sets ) { size_t cnt = 1; std::cout << " ** DEALT " << cards.size() << " CARDS: **\n"; for( std::vector<card>::iterator i = cards.begin(); i != cards.end(); i++ ) { std::cout << std::setw( 2 ) << cnt++ << ": " << ( *i ).toString() << "\n"; } std::cout << "\n ** CONTAINING " << sets.size() << " SETS: **\n"; for( std::vector<set>::iterator i = sets.begin(); i != sets.end(); i++ ) { for( size_t j = 0; j < ( *i ).index.size(); j++ ) { std::cout << " " << std::setiosflags( std::ios::left ) << std::setw( 34 ) << cards.at( ( *i ).index.at( j ) ).toString() << " : " << std::resetiosflags( std::ios::left ) << std::setw( 2 ) << ( *i ).index.at( j ) + 1 << "\n"; } std::cout << "\n"; } std::cout << "\n\n"; } int main( int argc, char* argv[] ) { srand( static_cast<unsigned>( time( NULL ) ) ); setPuzzle p; std::vector<card> v9, v12; std::vector<set> s4, s6; p.create( 9, 4, v9, s4 ); p.create( 12, 6, v12, s6 ); displayCardsSets( v9, s4 ); displayCardsSets( v12, s6 ); return 0; }
{{out}}
** DEALT 9 CARDS: **
1: [red three squiggle solid]
2: [purple three squiggle solid]
3: [red two diamond open]
4: [purple three oval striped]
5: [green one squiggle solid]
6: [green two diamond open]
7: [red one oval striped]
8: [green one diamond striped]
9: [purple one diamond open]
** CONTAINING 4 SETS: **
[red three squiggle solid] : 1
[red two diamond open] : 3
[red one oval striped] : 7
[purple three squiggle solid] : 2
[green two diamond open] : 6
[red one oval striped] : 7
[red two diamond open] : 3
[purple three oval striped] : 4
[green one squiggle solid] : 5
[green one squiggle solid] : 5
[red one oval striped] : 7
[purple one diamond open] : 9
** DEALT 12 CARDS: **
1: [green one diamond striped]
2: [red two squiggle solid]
3: [red three oval striped]
4: [red two diamond open]
5: [green three squiggle striped]
6: [red three squiggle striped]
7: [green two squiggle solid]
8: [purple two squiggle striped]
9: [purple one squiggle open]
10: [green one squiggle striped]
11: [purple three squiggle solid]
12: [red three squiggle open]
** CONTAINING 6 SETS: **
[green one diamond striped] : 1
[red three oval striped] : 3
[purple two squiggle striped] : 8
[red two squiggle solid] : 2
[green three squiggle striped] : 5
[purple one squiggle open] : 9
[green three squiggle striped] : 5
[purple three squiggle solid] : 11
[red three squiggle open] : 12
[red three squiggle striped] : 6
[green two squiggle solid] : 7
[purple one squiggle open] : 9
[red three squiggle striped] : 6
[purple two squiggle striped] : 8
[green one squiggle striped] : 10
[purple two squiggle striped] : 8
[purple one squiggle open] : 9
[purple three squiggle solid] : 11
Ceylon
Add import ceylon.random "1.3.3" to your module.ceylon file
import ceylon.random {
Random,
DefaultRandom
}
abstract class Feature() of Color  Symbol  NumberOfSymbols  Shading {}
abstract class Color()
of red  green  purple
extends Feature() {}
object red extends Color() {
string => "red";
}
object green extends Color() {
string => "green";
}
object purple extends Color() {
string => "purple";
}
abstract class Symbol()
of oval  squiggle  diamond
extends Feature() {}
object oval extends Symbol() {
string => "oval";
}
object squiggle extends Symbol() {
string => "squiggle";
}
object diamond extends Symbol() {
string => "diamond";
}
abstract class NumberOfSymbols()
of one  two  three
extends Feature() {}
object one extends NumberOfSymbols() {
string => "one";
}
object two extends NumberOfSymbols() {
string => "two";
}
object three extends NumberOfSymbols() {
string => "three";
}
abstract class Shading()
of solid  open  striped
extends Feature() {}
object solid extends Shading() {
string => "solid";
}
object open extends Shading() {
string => "open";
}
object striped extends Shading() {
string => "striped";
}
class Card(color, symbol, number, shading) {
shared Color color;
shared Symbol symbol;
shared NumberOfSymbols number;
shared Shading shading;
value plural => number == one then "" else "s";
string => "``number`` ``shading`` ``color`` ``symbol````plural``";
}
{Card*} deck = {
for(color in `Color`.caseValues)
for(symbol in `Symbol`.caseValues)
for(number in `NumberOfSymbols`.caseValues)
for(shading in `Shading`.caseValues)
Card(color, symbol, number, shading)
};
alias CardSet => [Card+];
Boolean validSet(CardSet cards) {
function allOrOne({Feature*} features) =>
let(uniques = features.distinct.size)
uniques == 3  uniques == 1;
return allOrOne(cards*.color) &&
allOrOne(cards*.number) &&
allOrOne(cards*.shading) &&
allOrOne(cards*.symbol);
}
{CardSet*} findSets(Card* cards) =>
cards
.sequence()
.combinations(3)
.filter(validSet);
Random random = DefaultRandom();
class Mode of basic  advanced {
shared Integer numberOfCards;
shared Integer numberOfSets;
shared new basic {
numberOfCards = 9;
numberOfSets = 4;
}
shared new advanced {
numberOfCards = 12;
numberOfSets = 6;
}
}
[{Card*}, {CardSet*}] deal(Mode mode) {
value randomStream = random.elements(deck);
while(true) {
value cards = randomStream.distinct.take(mode.numberOfCards).sequence();
value sets = findSets(*cards);
if(sets.size == mode.numberOfSets) {
return [cards, sets];
}
}
}
shared void run() {
value [cards, sets] = deal(Mode.basic);
print("The cards dealt are:
");
cards.each(print);
print("
Containing the sets:
");
for(cardSet in sets) {
cardSet.each(print);
print("");
}
}
D
Basic Version
import std.stdio, std.random, std.array, std.conv, std.traits, std.exception, std.range, std.algorithm; const class SetDealer { protected { enum Color: ubyte {green, purple, red} enum Number: ubyte {one, two, three} enum Symbol: ubyte {oval, diamond, squiggle} enum Fill: ubyte {open, striped, solid} static struct Card { Color c; Number n; Symbol s; Fill f; } static immutable Card[81] deck; } static this() pure nothrow @safe { immutable colors = [EnumMembers!Color]; immutable numbers = [EnumMembers!Number]; immutable symbols = [EnumMembers!Symbol]; immutable fill = [EnumMembers!Fill]; deck = deck.length.iota.map!(i => Card(colors[i / 27], numbers[(i / 9) % 3], symbols[(i / 3) % 3], fill[i % 3])).array; } // randomSample produces a sorted output that's convenient in our // case because we're printing to stout. Normally you would want // to shuffle. immutable(Card)[] deal(in uint numCards) const { enforce(numCards < deck.length, "Number of cards too large"); return deck[].randomSample(numCards).array; } // The summed enums of valid sets are always zero or a multiple // of 3. bool validSet(in ref Card c1, in ref Card c2, in ref Card c3) const pure nothrow @safe @nogc { return !((c1.c + c2.c + c3.c) % 3  (c1.n + c2.n + c3.n) % 3  (c1.s + c2.s + c3.s) % 3  (c1.f + c2.f + c3.f) % 3); } immutable(Card)[3][] findSets(in Card[] cards, in uint target = 0) const pure nothrow @safe { immutable len = cards.length; if (len < 3) return null; typeof(return) sets; foreach (immutable i; 0 .. len  2) foreach (immutable j; i + 1 .. len  1) foreach (immutable k; j + 1 .. len) if (validSet(cards[i], cards[j], cards[k])) { sets ~= [cards[i], cards[j], cards[k]]; if (target != 0 && sets.length > target) return null; } return sets; } } const final class SetPuzzleDealer : SetDealer { enum {basic = 9, advanced = 12} override immutable(Card)[] deal(in uint numCards = basic) const { immutable numSets = numCards / 2; typeof(return) cards; do { cards = super.deal(numCards); } while (findSets(cards, numSets).length != numSets); return cards; } } void main() { const dealer = new SetPuzzleDealer; const cards = dealer.deal; writefln("DEALT %d CARDS:", cards.length); writefln("%(%s\n%)", cards); immutable sets = dealer.findSets(cards); immutable len = sets.length; writefln("\nFOUND %d SET%s:", len, len == 1 ? "" : "S"); writefln("%(%(%s\n%)\n\n%)", sets); }
{{outSample output}}
DEALT 9 CARDS:
immutable(Card)(green, one, diamond, open)
immutable(Card)(green, two, diamond, open)
immutable(Card)(purple, one, diamond, striped)
immutable(Card)(purple, one, diamond, solid)
immutable(Card)(purple, two, squiggle, solid)
immutable(Card)(purple, three, oval, open)
immutable(Card)(red, one, diamond, solid)
immutable(Card)(red, one, squiggle, open)
immutable(Card)(red, three, oval, striped)
FOUND 4 SETS:
immutable(Card)(green, one, diamond, open)
immutable(Card)(purple, one, diamond, striped)
immutable(Card)(red, one, diamond, solid)
immutable(Card)(green, one, diamond, open)
immutable(Card)(purple, two, squiggle, solid)
immutable(Card)(red, three, oval, striped)
immutable(Card)(green, two, diamond, open)
immutable(Card)(purple, three, oval, open)
immutable(Card)(red, one, squiggle, open)
immutable(Card)(purple, one, diamond, striped)
immutable(Card)(purple, two, squiggle, solid)
immutable(Card)(purple, three, oval, open)
Short Version
This requires the third solution module of the Combinations Task.
void main() { import std.stdio, std.algorithm, std.range, std.random, combinations3; enum nDraw = 9, nGoal = nDraw / 2; auto deck = cartesianProduct("red green purple".split, "one two three".split, "oval squiggle diamond".split, "solid open striped".split).array; retry: auto draw = deck.randomSample(nDraw).map!(t => [t[]]).array; const sets = draw.combinations(3).filter!(cs => cs.dup .transposed.all!(t => t.array.sort().uniq.count % 2)).array; if (sets.length != nGoal) goto retry; writefln("Dealt %d cards:\n%(%(%8s %)\n%)\n", draw.length, draw); writefln("Containing:\n%(%(%(%8s %)\n%)\n\n%)", sets); }
{{out}}
Dealt 9 cards:
purple one oval solid
red three squiggle solid
purple three diamond solid
green one squiggle open
green two squiggle open
red two oval striped
purple one squiggle striped
purple two squiggle striped
green three diamond striped
Containing:
purple three diamond solid
green one squiggle open
red two oval striped
red three squiggle solid
green two squiggle open
purple one squiggle striped
red three squiggle solid
green one squiggle open
purple two squiggle striped
red two oval striped
purple one squiggle striped
green three diamond striped
EchoLisp
(require 'list)
;; a card is a vector [id color number symb shading], 0 <= id < 81
(define (makedeck (id 1))
(for*/vector(
[ color '(red green purple)]
[ number '(one two three)]
[ symb '( oval squiggle diamond)]
[ shading '(solid open striped)]) (++ id) (vector id color number symb shading)))
(define DECK (makedeck))
;; pregenerate 531441 ordered triples, among which 6561 are winners
(define TRIPLES (makevector (* 81 81 81)))
(define (maketriples )
(for* ((i 81)(j 81)(k 81))
(vectorset! TRIPLES (+ i (* 81 j) (* 6561 k))
(checkset [DECK i] [DECK j] [DECK k]))))
;; a deal is a list of cards id's.
(define (showdeal deal)
(for ((card deal)) (writeln [DECK card]))
(for ((set (combinations deal 3)))
(when
(checkset [DECK (first set)] [DECK (second set)][DECK (third set)])
(writeln 'winner set))))
;; rules of game here
(define (checkset cards: a b c)
(for ((i (inrange 1 5))) ;; each feature
#:continue (and (= [a i] [b i]) (= [a i] [c i]))
#:continue (and (!= [a i] [b i]) (!= [a i] [c i]) (!= [b i][c i]))
#:break #t => #f ))
;; sets = list of triples (cardid cardid cardid)
(define (countsets sets )
(for/sum ((s sets))
(if [TRIPLES ( + (first s) (* 81 (second s)) (* 6561 (third s)))]
1 0)))
;; task
(maketriples)
(define (play (n 9) (cmax 4) (sets) (deal))
(while #t
(set! deal (take (shuffle (iota 81)) n))
(set! sets (combinations deal 3))
#:break (= (countsets sets) cmax) => (showdeal deal)
))
{{out}}
(play) ;; The 94 game by default
#( 13 red two squiggle open)
#( 54 purple one oval solid)
#( 2 red one oval striped)
#( 15 red two diamond solid)
#( 53 green three diamond striped)
#( 48 green three squiggle solid)
#( 41 green two squiggle striped)
#( 66 purple two squiggle solid)
#( 64 purple two oval open)
winner (13 54 53)
winner (13 41 66)
winner (54 15 48)
winner (15 41 64)
;; 10 deals
(play 12 6)
#( 43 green two diamond open)
#( 16 red two diamond open)
#( 79 purple three diamond open)
#( 63 purple two oval solid)
#( 60 purple one diamond solid)
#( 75 purple three squiggle solid)
#( 64 purple two oval open)
#( 71 purple two diamond striped)
#( 67 purple two squiggle open)
#( 34 green one diamond open)
#( 59 purple one squiggle striped)
#( 54 purple one oval solid)
winner (16 79 34)
winner (79 63 59)
winner (79 60 71)
winner (63 60 75)
winner (63 71 67)
winner (75 67 59)
;; 31 deals
;; the (9 6) game is more difficult
#( 11 red two oval striped)
#( 9 red two oval solid)
#( 26 red three diamond striped)
#( 5 red one squiggle striped)
#( 60 purple one diamond solid)
#( 43 green two diamond open)
#( 10 red two oval open)
#( 67 purple two squiggle open)
#( 48 green three squiggle solid)
winner (11 9 10)
winner (11 26 5)
winner (9 60 48)
winner (26 60 43)
winner (5 67 48)
winner (43 10 67)
;; 17200 deals
Elixir
{{transRuby}}
defmodule RC do def set_puzzle(deal, goal) do {puzzle, sets} = get_puzzle_and_answer(deal, goal, produce_deck) IO.puts "Dealt #{length(puzzle)} cards:" print_cards(puzzle) IO.puts "Containing #{length(sets)} sets:" Enum.each(sets, fn set > print_cards(set) end) end defp get_puzzle_and_answer(hand_size, num_sets_goal, deck) do hand = Enum.take_random(deck, hand_size) sets = get_all_sets(hand) if length(sets) == num_sets_goal do {hand, sets} else get_puzzle_and_answer(hand_size, num_sets_goal, deck) end end defp get_all_sets(hand) do Enum.filter(comb(hand, 3), fn candidate > List.flatten(candidate) > Enum.group_by(&(&1)) > Map.values > Enum.all?(fn v > length(v) != 2 end) end) end defp print_cards(cards) do Enum.each(cards, fn card > :io.format " ~8s ~8s ~8s ~8s~n", card end) IO.puts "" end @colors ~w(red green purple)a @symbols ~w(oval squiggle diamond)a @numbers ~w(one two three)a @shadings ~w(solid open striped)a defp produce_deck do for color < @colors, symbol < @symbols, number < @numbers, shading < @shadings, do: [color, symbol, number, shading] end defp comb(_, 0), do: [[]] defp comb([], _), do: [] defp comb([ht], m) do (for l < comb(t, m1), do: [hl]) ++ comb(t, m) end end RC.set_puzzle(9, 4) RC.set_puzzle(12, 6)
{{out}}
Dealt 9 cards:
green oval one open
red oval one open
red oval two open
green diamond two striped
green diamond three open
green diamond one open
purple squiggle one open
red oval three solid
red oval three open
Containing 4 sets:
red oval one open
red oval two open
red oval three open
red oval one open
green diamond one open
purple squiggle one open
red oval two open
green diamond three open
purple squiggle one open
green diamond two striped
purple squiggle one open
red oval three solid
Dealt 12 cards:
purple oval one open
purple diamond two open
red oval three striped
purple diamond three striped
purple oval one solid
red oval two open
green diamond three open
green squiggle one solid
green oval three striped
red diamond two solid
red diamond one solid
green squiggle three striped
Containing 6 sets:
purple oval one open
red diamond two solid
green squiggle three striped
purple diamond two open
red oval three striped
green squiggle one solid
red oval three striped
purple diamond three striped
green squiggle three striped
purple diamond three striped
red oval two open
green squiggle one solid
purple oval one solid
red oval two open
green oval three striped
purple oval one solid
green squiggle one solid
red diamond one solid
Erlang
Until a better solution is found this is one.
module( set ). export( [deck/0, is_set/3, shuffle_deck/1, task/0] ). record( card, {number, symbol, shading, colour} ). deck() > [#card{number=N, symbol=Sy, shading=Sh, colour=C}  N < [1,2,3], Sy < [diamond, squiggle, oval], Sh < [solid, striped, open], C < [red, green, purple]]. is_set( Card1, Card2, Card3 ) > is_colour_correct( Card1, Card2, Card3 ) andalso is_number_correct( Card1, Card2, Card3 ) andalso is_shading_correct( Card1, Card2, Card3 ) andalso is_symbol_correct( Card1, Card2, Card3 ). shuffle_deck( Deck ) > knuth_shuffle:list( Deck ). task() > basic(), advanced(). advanced() > common( 6, 12 ). basic() > common( 4, 9 ). common( X, Y ) > {Sets, Cards} = find_x_sets_in_y_cards( X, Y, deck() ), io:fwrite( "Cards ~p~n", [Cards] ), io:fwrite( "Gives sets:~n" ), [io:fwrite( "~p~n", [S] )  S < Sets]. find_x_sets_in_y_cards( X, Y, Deck ) > {Cards, _T} = lists:split( Y, shuffle_deck(Deck) ), find_x_sets_in_y_cards( X, Y, Cards, make_sets1(Cards, []) ). find_x_sets_in_y_cards( X, _Y, _Deck, Cards, Sets ) when erlang:length(Sets) =:= X > {Sets, Cards}; find_x_sets_in_y_cards( X, Y, Deck, _Cards, _Sets ) > find_x_sets_in_y_cards( X, Y, Deck ). is_colour_correct( Card1, Card2, Card3 ) > is_colour_different( Card1, Card2, Card3 ) orelse is_colour_same( Card1, Card2, Card3 ). is_colour_different( #card{colour=C1}, #card{colour=C2}, #card{colour=C3} ) when C1 =/= C2, C1 =/= C3, C2 =/= C3 > true; is_colour_different( _Card1, _Card2, _Card3 ) > false. is_colour_same( #card{colour=C}, #card{colour=C}, #card{colour=C} ) > true; is_colour_same( _Card1, _Card2, _Card3 ) > false. is_number_correct( Card1, Card2, Card3 ) > is_number_different( Card1, Card2, Card3 ) orelse is_number_same( Card1, Card2, Card3 ). is_number_different( #card{number=N1}, #card{number=N2}, #card{number=N3} ) when N1 =/= N2, N1 =/= N3, N2 =/= N3 > true; is_number_different( _Card1, _Card2, _Card3 ) > false. is_number_same( #card{number=N}, #card{number=N}, #card{number=N} ) > true; is_number_same( _Card1, _Card2, _Card3 ) > false. is_shading_correct( Card1, Card2, Card3 ) > is_shading_different( Card1, Card2, Card3 ) orelse is_shading_same( Card1, Card2, Card3 ). is_shading_different( #card{shading=S1}, #card{shading=S2}, #card{shading=S3} ) when S1 =/= S2, S1 =/= S3, S2 =/= S3 > true; is_shading_different( _Card1, _Card2, _Card3 ) > false. is_shading_same( #card{shading=S}, #card{shading=S}, #card{shading=S} ) > true; is_shading_same( _Card1, _Card2, _Card3 ) > false. is_symbol_correct( Card1, Card2, Card3 ) > is_symbol_different( Card1, Card2, Card3 ) orelse is_symbol_same( Card1, Card2, Card3 ). is_symbol_different( #card{symbol=S1}, #card{symbol=S2}, #card{symbol=S3} ) when S1 =/= S2, S1 =/= S3, S2 =/= S3 > true; is_symbol_different( _Card1, _Card2, _Card3 ) > false. is_symbol_same( #card{symbol=S}, #card{symbol=S}, #card{symbol=S} ) > true; is_symbol_same( _Card1, _Card2, _Card3 ) > false. %% Nested loops 1, 2 and 3 make_sets1( [_Second_to_last, _Last], Sets ) > Sets; make_sets1( [Card  T], Sets ) > make_sets1( T, make_sets2(Card, T, Sets) ). make_sets2( _Card, [_Last], Sets ) > Sets; make_sets2( Card1, [Card2  T], Sets ) > make_sets2( Card1, T, make_sets3( Card1, Card2, T, Sets) ). make_sets3( _Card1, _Card2, [], Sets ) > Sets; make_sets3( Card1, Card2, [Card3  T], Sets ) > make_sets3( Card1, Card2, T, make_sets_acc(is_set(Card1, Card2, Card3), {Card1, Card2, Card3}, Sets) ). make_sets_acc( true, Set, Sets ) > [Set  Sets]; make_sets_acc( false, _Set, Sets ) > Sets.
{{out}}
53> set:task().
Cards [{card,2,diamond,striped,purple},
{card,3,squiggle,solid,purple},
{card,2,squiggle,open,red},
{card,3,oval,solid,purple},
{card,1,diamond,striped,green},
{card,1,oval,open,purple},
{card,3,squiggle,striped,purple},
{card,2,diamond,solid,purple},
{card,1,oval,striped,purple}]
Gives sets:
{{card,1,oval,open,purple},
{card,3,squiggle,striped,purple},
{card,2,diamond,solid,purple}}
{{card,2,squiggle,open,red},
{card,3,oval,solid,purple},
{card,1,diamond,striped,green}}
{{card,2,diamond,striped,purple},
{card,3,squiggle,striped,purple},
{card,1,oval,striped,purple}}
{{card,2,diamond,striped,purple},
{card,3,squiggle,solid,purple},
{card,1,oval,open,purple}}
Cards [{card,1,diamond,striped,purple},
{card,3,diamond,solid,purple},
{card,2,diamond,solid,green},
{card,1,diamond,open,green},
{card,3,oval,striped,red},
{card,3,squiggle,striped,red},
{card,2,oval,solid,purple},
{card,1,squiggle,open,green},
{card,3,diamond,solid,green},
{card,2,diamond,striped,red},
{card,2,squiggle,solid,purple},
{card,3,oval,open,purple}]
Gives sets:
{{card,3,squiggle,striped,red},
{card,3,diamond,solid,green},
{card,3,oval,open,purple}}
{{card,3,squiggle,striped,red},
{card,1,squiggle,open,green},
{card,2,squiggle,solid,purple}}
{{card,1,diamond,open,green},
{card,3,squiggle,striped,red},
{card,2,oval,solid,purple}}
{{card,1,diamond,open,green},
{card,3,oval,striped,red},
{card,2,squiggle,solid,purple}}
{{card,3,diamond,solid,purple},
{card,1,diamond,open,green},
{card,2,diamond,striped,red}}
{{card,1,diamond,striped,purple},
{card,2,squiggle,solid,purple},
{card,3,oval,open,purple}}
=={{headerF SharpF#}}==
open System type Number = One  Two  Three type Color = Red  Green  Purple type Fill = Solid  Open  Striped type Symbol = Oval  Squiggle  Diamond type Card = { Number: Number; Color: Color; Fill: Fill; Symbol: Symbol } // A 'Set' is 3 cards in which each individual feature is either all the SAME on each card, OR all DIFFERENT on each card. let SetSize = 3 type CardsGenerator() = let _rand = Random() let shuffleInPlace data = Array.sortInPlaceBy (fun _ > (_rand.Next(0, Array.length data))) data let createCards() = [ for n in [One; Two; Three] do for c in [Red; Green; Purple] do for f in [Solid; Open; Striped] do for s in [Oval; Squiggle; Diamond] do yield { Number = n; Color = c; Fill = f; Symbol = s } ] let _cards = createCards() member x.GetHand cardCount = shuffleInPlace _cards Seq.take cardCount _cards > Seq.toList // Find all the combinations of n elements let rec combinations n items = match n, items with  0, _ > [[]]  _, [] > []  k, (x::xs) > List.map ((@) [x]) (combinations (k1) xs) @ combinations k xs let validCardSet (cards: Card list) = // Valid feature if all features are the same or different let validFeature = function  [a; b; c] > (a = b && b = c)  (a <> b && a <> c && b <> c)  _ > false // Build and validate the feature lists let isValid = cards > List.fold (fun (ns, cs, fs, ss) c > (c.Number::ns, c.Color::cs, c.Fill::fs, c.Symbol::ss)) ([], [], [], []) > fun (ns, cs, fs, ss) > (validFeature ns) && (validFeature cs) && (validFeature fs) && (validFeature ss) if isValid then Some cards else None let findSolution cardCount setCount = let cardsGen = CardsGenerator() let rec search () = let hand = cardsGen.GetHand cardCount let foundSets = combinations SetSize hand > List.choose validCardSet if foundSets.Length = setCount then (hand, foundSets) else search() search() let displaySolution (hand: Card list, sets: Card list list) = let printCardDetails (c: Card) = printfn " %A %A %A %A" c.Number c.Color c.Symbol c.Fill printfn "Dealt %d cards:" hand.Length List.iter printCardDetails hand printf "\n" printfn "Found %d sets:" sets.Length sets > List.iter (fun cards > List.iter printCardDetails cards; printf "\n" ) let playGame() = let solve cardCount setCount = displaySolution (findSolution cardCount setCount) solve 9 4 solve 12 6 playGame()
Output:
Dealt 9 cards:
Three Red Diamond Solid
Two Red Oval Solid
Three Red Oval Striped
Two Purple Oval Striped
One Green Squiggle Open
One Purple Diamond Solid
One Green Oval Striped
One Green Diamond Solid
Three Purple Diamond Striped
Found 4 sets:
Three Red Diamond Solid
Two Purple Oval Striped
One Green Squiggle Open
Two Red Oval Solid
One Green Squiggle Open
Three Purple Diamond Striped
Three Red Oval Striped
Two Purple Oval Striped
One Green Oval Striped
One Green Squiggle Open
One Green Oval Striped
One Green Diamond Solid
Dealt 12 cards:
One Green Diamond Open
Two Red Diamond Striped
Three Red Oval Striped
One Red Diamond Open
Three Green Oval Open
Two Purple Squiggle Solid
Two Red Oval Striped
One Red Oval Striped
Two Red Oval Open
Three Purple Oval Striped
One Purple Diamond Open
Three Red Oval Solid
Found 6 sets:
One Green Diamond Open
Three Red Oval Striped
Two Purple Squiggle Solid
One Green Diamond Open
One Red Diamond Open
One Purple Diamond Open
Three Red Oval Striped
Two Red Oval Striped
One Red Oval Striped
Three Green Oval Open
Three Purple Oval Striped
Three Red Oval Solid
Two Purple Squiggle Solid
Three Purple Oval Striped
One Purple Diamond Open
One Red Oval Striped
Two Red Oval Open
Three Red Oval Solid
Factor
USING: arrays backtrack combinators.shortcircuit formatting
fry grouping io kernel literals math.combinatorics math.matrices
prettyprint qw random sequences sets ;
IN: rosettacode.setpuzzle
CONSTANT: deck $[
[
qw{ red green purple } amblazy
qw{ one two three } amblazy
qw{ oval squiggle diamond } amblazy
qw{ solid open striped } amblazy 4array
] bagof
]
: validcategory? ( seq  ? )
{ [ allequal? ] [ allunique? ] } 1 ;
: validset? ( seq  ? )
[ validcategory? ] columnmap t [ and ] reduce ;
: findsets ( seq  seq )
3 <combinations> [ validset? ] filter ;
: dealhand ( m n  seq valid? )
[ deck swap sample ] dip over findsets length = ;
: findvalidhand ( m n  seq )
[ f ] 2dip '[ drop _ _ dealhand not ] loop ;
: setpuzzle ( m n  )
[ findvalidhand ] 2keep
[ "Dealt %d cards:\n" printf simpletable. nl ]
[
"Containing %d sets:\n" printf findsets
{ { " " " " " " " " } } join simpletable. nl
] bicurry* bi ;
: main (  )
9 4 setpuzzle
12 6 setpuzzle ;
MAIN: main
{{out}}
Dealt 9 cards: purple one diamond striped purple three squiggle open purple one oval solid green two squiggle striped red one oval striped green three oval solid purple three diamond striped red two oval striped purple two diamond striped Containing 4 sets: purple one diamond striped purple three diamond striped purple two diamond striped purple three squiggle open purple one oval solid purple two diamond striped green two squiggle striped red one oval striped purple three diamond striped green two squiggle striped red two oval striped purple two diamond striped Dealt 12 cards: green one oval striped red two squiggle striped red two diamond open purple two oval solid green three squiggle open purple one squiggle striped purple two squiggle open red two squiggle solid red three oval open purple one oval solid red one diamond striped red two oval striped Containing 6 sets: green one oval striped purple two oval solid red three oval open green one oval striped purple one squiggle striped red one diamond striped red two diamond open red two squiggle solid red two oval striped purple two oval solid green three squiggle open red one diamond striped green three squiggle open purple one squiggle striped red two squiggle solid red two squiggle solid red three oval open red one diamond striped ``` ## Go ```go package main import ( "fmt" "math/rand" "time" ) const ( number = [3]string{"1", "2", "3"} color = [3]string{"red", "green", "purple"} shade = [3]string{"solid", "open", "striped"} shape = [3]string{"oval", "squiggle", "diamond"} ) type card int func (c card) String() string { return fmt.Sprintf("%s %s %s %s", number[c/27], color[c/9%3], shade[c/3%3], shape[c%3]) } func main() { rand.Seed(time.Now().Unix()) game("Basic", 9, 4) game("Advanced", 12, 6) } func game(level string, cards, sets int) { // create deck d := make([]card, 81) for i := range d { d[i] = card(i) } var found [][3]card for len(found) != sets { found = found[:0] // deal for i := 0; i < cards; i++ { j := rand.Intn(81  i) d[i], d[j] = d[j], d[i] } // consider all triplets for i := 2; i < cards; i++ { c1 := d[i] for j := 1; j < i; j++ { c2 := d[j] l3: for _, c3 := range d[:j] { for f := card(1); f < 81; f *= 3 { if (c1/f%3 + c2/f%3 + c3/f%3) % 3 != 0 { continue l3 // not a set } } // it's a set found = append(found, [3]card{c1, c2, c3}) } } } } // found the right number fmt.Printf("%s game. %d cards, %d sets.\n", level, cards, sets) fmt.Println("Cards:") for _, c := range d[:cards] { fmt.Println(" ", c) } fmt.Println("Sets:") for _, s := range found { fmt.Printf(" %s\n %s\n %s\n",s[0],s[1],s[2]) } } ``` {{out}} ```txt Basic game. 9 cards, 4 sets. Cards: 3 red solid oval 3 red open oval 3 purple striped oval 2 green striped oval 2 red solid oval 1 purple open diamond 2 purple solid squiggle 1 green striped diamond 3 green striped squiggle Sets: 2 purple solid squiggle 1 purple open diamond 3 purple striped oval 1 green striped diamond 2 purple solid squiggle 3 red open oval 3 green striped squiggle 1 purple open diamond 2 red solid oval 3 green striped squiggle 1 green striped diamond 2 green striped oval Advanced game. 12 cards, 6 sets. Cards: 2 green solid squiggle 3 red solid oval 3 purple open oval 2 purple open squiggle 3 red striped oval 1 red open oval 1 purple open diamond 1 green striped squiggle 3 red open oval 3 red striped squiggle 2 red striped oval 1 purple solid diamond Sets: 1 purple open diamond 2 purple open squiggle 3 purple open oval 1 purple open diamond 3 red striped oval 2 green solid squiggle 3 red open oval 3 red striped oval 3 red solid oval 2 red striped oval 1 red open oval 3 red solid oval 1 purple solid diamond 3 red solid oval 2 green solid squiggle 1 purple solid diamond 1 green striped squiggle 1 red open oval ``` ## Haskell ```haskell import Control.Monad.State (State, evalState, replicateM, runState, state) import System.Random (StdGen, newStdGen, randomR) import Data.List (find, nub, sort) combinations :: Int > [a] > [[a]] combinations 0 _ = [[]] combinations _ [] = [] combinations k (y:ys) = map (y :) (combinations (k  1) ys) ++ combinations k ys data Color = Red  Green  Purple deriving (Show, Enum, Bounded, Ord, Eq) data Symbol = Oval  Squiggle  Diamond deriving (Show, Enum, Bounded, Ord, Eq) data Count = One  Two  Three deriving (Show, Enum, Bounded, Ord, Eq) data Shading = Solid  Open  Striped deriving (Show, Enum, Bounded, Ord, Eq) data Card = Card { color :: Color , symbol :: Symbol , count :: Count , shading :: Shading } deriving (Show)  Identify a set of three cards by counting all attribute types.  if each count is 3 or 1 ( not 2 ) the the cards compose a set. isSet :: [Card] > Bool isSet cs = let total = length . nub . sort . flip map cs in notElem 2 [total color, total symbol, total count, total shading]  Get a random card from a deck. Returns the card and removes it from the deck. getCard :: State (StdGen, [Card]) Card getCard = state $ \(gen, cs) > let (i, newGen) = randomR (0, length cs  1) gen (a, b) = splitAt i cs in (head b, (newGen, a ++ tail b))  Get a hand of cards. Starts with new deck and then removes the  appropriate number of cards from that deck. getHand :: Int > State StdGen [Card] getHand n = state $ \gen > let az = [minBound .. maxBound] deck = [ Card co sy ct sh  co < az , sy < az , ct < az , sh < az ] (a, (newGen, _)) = runState (replicateM n getCard) (gen, deck) in (a, newGen)  Get an unbounded number of hands of the appropriate number of cards. getManyHands :: Int > State StdGen [[Card]] getManyHands n = (sequence . repeat) (getHand n)  Deal out hands of the appropriate size until one with the desired number  of sets is found. then print the hand and the sets. showSolutions :: Int > Int > IO () showSolutions cardCount solutionCount = do putStrLn $ "Showing hand of " ++ show cardCount ++ " cards with " ++ show solutionCount ++ " solutions." gen < newStdGen let Just z = find ((solutionCount ==) . length . filter isSet . combinations 3) $ evalState (getManyHands cardCount) gen mapM_ print z putStrLn "" putStrLn "Solutions:" mapM_ putSet $ filter isSet $ combinations 3 z where putSet st = do mapM_ print st putStrLn ""  Show a hand of 9 cards with 4 solutions  and a hand of 12 cards with 6 solutions. main :: IO () main = do showSolutions 9 4 showSolutions 12 6 ``` {{out}}Showing hand of 9 cards with 4 solutions. Card {color = Red, symbol = Diamond, count = Two, shading = Open} Card {color = Purple, symbol = Diamond, count = Two, shading = Open} Card {color = Red, symbol = Oval, count = Two, shading = Open} Card {color = Green, symbol = Squiggle, count = Two, shading = Striped} Card {color = Red, symbol = Squiggle, count = Two, shading = Open} Card {color = Red, symbol = Diamond, count = One, shading = Striped} Card {color = Green, symbol = Diamond, count = Three, shading = Solid} Card {color = Purple, symbol = Squiggle, count = One, shading = Solid} Card {color = Purple, symbol = Oval, count = Three, shading = Striped} Solutions: Card {color = Red, symbol = Diamond, count = Two, shading = Open} Card {color = Red, symbol = Oval, count = Two, shading = Open} Card {color = Red, symbol = Squiggle, count = Two, shading = Open} Card {color = Purple, symbol = Diamond, count = Two, shading = Open} Card {color = Red, symbol = Diamond, count = One, shading = Striped} Card {color = Green, symbol = Diamond, count = Three, shading = Solid} Card {color = Purple, symbol = Diamond, count = Two, shading = Open} Card {color = Purple, symbol = Squiggle, count = One, shading = Solid} Card {color = Purple, symbol = Oval, count = Three, shading = Striped} Card {color = Green, symbol = Squiggle, count = Two, shading = Striped} Card {color = Red, symbol = Diamond, count = One, shading = Striped} Card {color = Purple, symbol = Oval, count = Three, shading = Striped} Showing hand of 12 cards with 6 solutions. Card {color = Purple, symbol = Oval, count = Two, shading = Solid} Card {color = Green, symbol = Squiggle, count = Two, shading = Striped} Card {color = Purple, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Squiggle, count = One, shading = Open} Card {color = Green, symbol = Oval, count = Two, shading = Open} Card {color = Green, symbol = Oval, count = One, shading = Open} Card {color = Green, symbol = Squiggle, count = Three, shading = Solid} Card {color = Red, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Oval, count = One, shading = Solid} Card {color = Red, symbol = Squiggle, count = Two, shading = Open} Card {color = Green, symbol = Oval, count = Three, shading = Open} Solutions: Card {color = Purple, symbol = Oval, count = Two, shading = Solid} Card {color = Green, symbol = Squiggle, count = Two, shading = Striped} Card {color = Red, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Squiggle, count = Two, shading = Striped} Card {color = Green, symbol = Squiggle, count = One, shading = Open} Card {color = Green, symbol = Squiggle, count = Three, shading = Solid} Card {color = Purple, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Oval, count = Two, shading = Open} Card {color = Red, symbol = Squiggle, count = Two, shading = Open} Card {color = Purple, symbol = Diamond, count = Two, shading = Open} Card {color = Red, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Squiggle, count = One, shading = Open} Card {color = Green, symbol = Diamond, count = Two, shading = Open} Card {color = Green, symbol = Oval, count = Three, shading = Open} Card {color = Green, symbol = Oval, count = Two, shading = Open} Card {color = Green, symbol = Oval, count = One, shading = Open} Card {color = Green, symbol = Oval, count = Three, shading = Open} ``` ## J '''Solution:''' ```j require 'stats/base' Number=: ;:'one two three' Colour=: ;:'red green purple' Fill=: ;:'solid open striped' Symbol=: ;:'oval squiggle diamond' Features=: Number ; Colour ; Fill ;< Symbol Deck=: > ; <"1 { i.@#&.> Features sayCards=: (', ' joinstring Features {&>~ ])"1 drawRandom=: ] {~ (? #) isSet=: *./@:(1 3 e.~ [: #@~."1 :)"2 getSets=: [: (] #~ isSet) ] {~ 3 comb # countSets=: #@:getSets set_puzzle=: verb define target=. <. : y whilst. target ~: countSets Hand do. Hand=. y drawRandom Deck end. echo 'Dealt ',(": y),' Cards:' echo sayCards sort Hand echo LF,'Found ',(":target),' Sets:' echo sayCards sort"2 getSets Hand ) ``` '''Example:''' ```j set_puzzle 9 Dealt 9 Cards: one, red, solid, oval one, green, open, squiggle two, purple, striped, squiggle three, red, solid, squiggle three, red, open, oval three, green, solid, oval three, green, open, diamond three, purple, open, oval three, purple, striped, oval Found 4 Sets: three, red, solid, squiggle three, green, open, diamond three, purple, striped, oval one, red, solid, oval two, purple, striped, squiggle three, green, open, diamond one, green, open, squiggle two, purple, striped, squiggle three, red, solid, squiggle three, red, open, oval three, green, solid, oval three, purple, striped, oval ``` ## Java ```java import java.util.*; public class SetPuzzle { enum Color { GREEN(0), PURPLE(1), RED(2); private Color(int v) { val = v; } public final int val; } enum Number { ONE(0), TWO(1), THREE(2); private Number(int v) { val = v; } public final int val; } enum Symbol { OVAL(0), DIAMOND(1), SQUIGGLE(2); private Symbol(int v) { val = v; } public final int val; } enum Fill { OPEN(0), STRIPED(1), SOLID(2); private Fill(int v) { val = v; } public final int val; } private static class Card implements Comparable{ Color c; Number n; Symbol s; Fill f; @Override public String toString() { return String.format("[Card: %s, %s, %s, %s]", c, n, s, f); } @Override public int compareTo(Card o) { return (c.val  o.c.val) * 10 + (n.val  o.n.val); } } private static Card[] deck; public static void main(String[] args) { deck = new Card[81]; Color[] colors = Color.values(); Number[] numbers = Number.values(); Symbol[] symbols = Symbol.values(); Fill[] fillmodes = Fill.values(); for (int i = 0; i < deck.length; i++) { deck[i] = new Card(); deck[i].c = colors[i / 27]; deck[i].n = numbers[(i / 9) % 3]; deck[i].s = symbols[(i / 3) % 3]; deck[i].f = fillmodes[i % 3]; } findSets(12); } private static void findSets(int numCards) { int target = numCards / 2; Card[] cards; Card[][] sets = new Card[target][3]; int cnt; do { Collections.shuffle(Arrays.asList(deck)); cards = Arrays.copyOfRange(deck, 0, numCards); cnt = 0; outer: for (int i = 0; i < cards.length  2; i++) { for (int j = i + 1; j < cards.length  1; j++) { for (int k = j + 1; k < cards.length; k++) { if (validSet(cards[i], cards[j], cards[k])) { if (cnt < target) sets[cnt] = new Card[]{cards[i], cards[j], cards[k]}; if (++cnt > target) { break outer; } } } } } } while (cnt != target); Arrays.sort(cards); System.out.printf("GIVEN %d CARDS:\n\n", numCards); for (Card c : cards) { System.out.println(c); } System.out.println(); System.out.println("FOUND " + target + " SETS:\n"); for (Card[] set : sets) { for (Card c : set) { System.out.println(c); } System.out.println(); } } private static boolean validSet(Card c1, Card c2, Card c3) { int tot = 0; tot += (c1.c.val + c2.c.val + c3.c.val) % 3; tot += (c1.n.val + c2.n.val + c3.n.val) % 3; tot += (c1.s.val + c2.s.val + c3.s.val) % 3; tot += (c1.f.val + c2.f.val + c3.f.val) % 3; return tot == 0; } } ``` ```txt GIVEN 12 CARDS: [Card: GREEN, ONE, DIAMOND, OPEN] [Card: GREEN, TWO, SQUIGGLE, OPEN] [Card: GREEN, THREE, DIAMOND, STRIPED] [Card: GREEN, THREE, DIAMOND, OPEN] [Card: PURPLE, ONE, DIAMOND, SOLID] [Card: PURPLE, ONE, SQUIGGLE, SOLID] [Card: PURPLE, TWO, SQUIGGLE, SOLID] [Card: PURPLE, THREE, DIAMOND, OPEN] [Card: RED, ONE, SQUIGGLE, STRIPED] [Card: RED, ONE, OVAL, STRIPED] [Card: RED, TWO, DIAMOND, STRIPED] [Card: RED, THREE, OVAL, STRIPED] FOUND 6 SETS: [Card: GREEN, TWO, SQUIGGLE, OPEN] [Card: PURPLE, ONE, DIAMOND, SOLID] [Card: RED, THREE, OVAL, STRIPED] [Card: GREEN, THREE, DIAMOND, OPEN] [Card: RED, ONE, OVAL, STRIPED] [Card: PURPLE, TWO, SQUIGGLE, SOLID] [Card: GREEN, THREE, DIAMOND, OPEN] [Card: PURPLE, ONE, DIAMOND, SOLID] [Card: RED, TWO, DIAMOND, STRIPED] [Card: RED, ONE, SQUIGGLE, STRIPED] [Card: RED, THREE, OVAL, STRIPED] [Card: RED, TWO, DIAMOND, STRIPED] [Card: RED, ONE, OVAL, STRIPED] [Card: PURPLE, ONE, SQUIGGLE, SOLID] [Card: GREEN, ONE, DIAMOND, OPEN] [Card: GREEN, ONE, DIAMOND, OPEN] [Card: RED, THREE, OVAL, STRIPED] [Card: PURPLE, TWO, SQUIGGLE, SOLID] ``` ## Julia Plays one basic game and one advanced game. ```julia using Random, IterTools, Combinatorics function SetGameTM(basic = true) drawsize = basic ? 9 : 12 setsneeded = div(drawsize, 2) setsof3 = Vector{Vector{NTuple{4, String}}}() draw = Vector{NTuple{4, String}}() deck = collect(Iterators.product(["red", "green", "purple"], ["one", "two", "three"], ["oval", "squiggle", "diamond"], ["solid", "open", "striped"])) while length(setsof3) != setsneeded empty!(draw) empty!(setsof3) map(x > push!(draw, x), shuffle(deck)[1:drawsize]) for threecards in combinations(draw, 3) canuse = true for i in 1:4 u = length(unique(map(x>x[i], threecards))) if u != 3 && u != 1 canuse = false end end if canuse push!(setsof3, threecards) end end end println("Dealt $drawsize cards:") for card in draw println(" $card") end println("\nFormed these cards into $setsneeded sets:") for set in setsof3 for card in set println(" $card") end println() end end SetGameTM() SetGameTM(false) ``` {{output}} ```txt Dealt 9 cards: ("green", "one", "oval", "open") ("green", "three", "diamond", "open") ("purple", "one", "diamond", "striped") ("purple", "three", "oval", "solid") ("red", "two", "diamond", "open") ("red", "one", "oval", "striped") ("green", "one", "squiggle", "striped") ("green", "two", "oval", "solid") ("purple", "two", "squiggle", "open") Formed these cards into 4 sets: ("green", "three", "diamond", "open") ("green", "one", "squiggle", "striped") ("green", "two", "oval", "solid") ("purple", "one", "diamond", "striped") ("purple", "three", "oval", "solid") ("purple", "two", "squiggle", "open") ("purple", "one", "diamond", "striped") ("red", "one", "oval", "striped") ("green", "one", "squiggle", "striped") ("purple", "three", "oval", "solid") ("red", "two", "diamond", "open") ("green", "one", "squiggle", "striped") Dealt 12 cards: ("red", "one", "squiggle", "open") ("green", "one", "diamond", "striped") ("red", "two", "oval", "solid") ("green", "three", "squiggle", "striped") ("green", "three", "squiggle", "open") ("red", "one", "oval", "solid") ("purple", "two", "oval", "striped") ("green", "two", "oval", "striped") ("green", "three", "oval", "open") ("purple", "two", "diamond", "open") ("purple", "three", "diamond", "striped") ("purple", "two", "squiggle", "solid") Formed these cards into 6 sets: ("red", "one", "squiggle", "open") ("green", "three", "squiggle", "striped") ("purple", "two", "squiggle", "solid") ("red", "one", "squiggle", "open") ("green", "three", "oval", "open") ("purple", "two", "diamond", "open") ("green", "one", "diamond", "striped") ("green", "three", "squiggle", "striped") ("green", "two", "oval", "striped") ("green", "three", "squiggle", "striped") ("red", "one", "oval", "solid") ("purple", "two", "diamond", "open") ("red", "one", "oval", "solid") ("purple", "two", "oval", "striped") ("green", "three", "oval", "open") ("purple", "two", "oval", "striped") ("purple", "two", "diamond", "open") ("purple", "two", "squiggle", "solid") ``` ## Kotlin ```scala // version 1.1.3 import java.util.Collections.shuffle enum class Color { RED, GREEN, PURPLE } enum class Symbol { OVAL, SQUIGGLE, DIAMOND } enum class Number { ONE, TWO, THREE } enum class Shading { SOLID, OPEN, STRIPED } enum class Degree { BASIC, ADVANCED } class Card( val color: Color, val symbol: Symbol, val number: Number, val shading: Shading ) : Comparable { private val value = color.ordinal * 27 + symbol.ordinal * 9 + number.ordinal * 3 + shading.ordinal override fun compareTo(other: Card) = value.compareTo(other.value) override fun toString() = ( color.name.padEnd(8) + symbol.name.padEnd(10) + number.name.padEnd(7) + shading.name.padEnd(7) ).toLowerCase() companion object { val zero = Card(Color.RED, Symbol.OVAL, Number.ONE, Shading.SOLID) } } fun createDeck() = List (81) { val col = Color.values() [it / 27] val sym = Symbol.values() [it / 9 % 3] val num = Number.values() [it / 3 % 3] val shd = Shading.values()[it % 3] Card(col, sym, num, shd) } fun playGame(degree: Degree) { val deck = createDeck() val nCards = if (degree == Degree.BASIC) 9 else 12 val nSets = nCards / 2 val sets = Array(nSets) { Array(3) { Card.zero } } var hand: Array outer@ while (true) { shuffle(deck) hand = deck.take(nCards).toTypedArray() var count = 0 for (i in 0 until hand.size  2) { for (j in i + 1 until hand.size  1) { for (k in j + 1 until hand.size) { val trio = arrayOf(hand[i], hand[j], hand[k]) if (isSet(trio)) { sets[count++] = trio if (count == nSets) break@outer } } } } } hand.sort() println("DEALT $nCards CARDS:\n") println(hand.joinToString("\n")) println("\nCONTAINING $nSets SETS:\n") for (s in sets) { s.sort() println(s.joinToString("\n")) println() } } fun isSet(trio: Array ): Boolean { val r1 = trio.sumBy { it.color.ordinal } % 3 val r2 = trio.sumBy { it.symbol.ordinal } % 3 val r3 = trio.sumBy { it.number.ordinal } % 3 val r4 = trio.sumBy { it.shading.ordinal } % 3 return (r1 + r2 + r3 + r4) == 0 } fun main(args: Array ) { playGame(Degree.BASIC) println() playGame(Degree.ADVANCED) } ``` Sample output: ```txt DEALT 9 CARDS: red oval three solid red diamond two solid green oval one open green oval three open green squiggle one open green diamond one open purple oval three striped purple squiggle three solid purple diamond two striped CONTAINING 4 SETS: red oval three solid green squiggle one open purple diamond two striped red oval three solid green oval three open purple oval three striped green oval one open green squiggle one open green diamond one open red diamond two solid green squiggle one open purple oval three striped DEALT 12 CARDS: red squiggle two solid red diamond two solid red diamond two open red diamond two striped green oval one open green oval three solid green oval three open green squiggle one solid green diamond one striped purple oval one solid purple oval three open purple squiggle one striped CONTAINING 6 SETS: red diamond two open green oval three solid purple squiggle one striped red diamond two solid red diamond two open red diamond two striped red diamond two solid green oval three open purple squiggle one striped red squiggle two solid green diamond one striped purple oval three open green oval one open green squiggle one solid green diamond one striped red diamond two striped green squiggle one solid purple oval three open ``` ## Mathematica A simple brute force approach. This code highlights two things: 1) a few of Mathematica's "higherlevel" functions such as Tuples and Subsets and 2) the straightforwardness enabled by the language's "dynamic typing" (more precisely, its symbolic semantics) and its usage of lists for everything (in this particular example, the fact that functions such as Tuples and Entropy can be used on lists with arbitrary content). ```Mathematica colors = {Red, Green, Purple}; symbols = {"0", "\[TildeTilde]", "\[Diamond]"}; numbers = {1, 2, 3}; shadings = {"\[FilledSquare]", "\[Square]", "\[DoublePrime]"}; validTripleQ[l_List] := Entropy[l] != Entropy[{1, 1, 2}]; validSetQ[cards_List] := And @@ (validTripleQ /@ Transpose[cards]); allCards = Tuples[{colors, symbols, numbers, shadings}]; deal[{numDeal_, setNum_}] := Module[{cards, count = 0}, While[count != setNum, cards = RandomSample[allCards, numDeal]; count = Count[Subsets[cards, {3}], _?validSetQ]]; cards]; Row[{Style[#2, #1], #3, #4}] & @@@ deal[{9, 4}] ``` ## PARI/GP ```parigp dealraw(cards)=vector(cards,i,vector(4,j,1< sets,return(0)) ))); if(#S==sets,Vec(S),0) }; deal(cards,sets)={ my(v,s); until(s, s=check(v=dealraw(cards),sets) ); v=apply(name,v); for(i=1,cards,print(v[i])); for(i=1,sets, print("Set #"i); for(j=1,3,print(" "v[s[i][j]])) ) }; deal(9,4) deal(12,6) ``` {{output}} ```txt green, diamond, one, open purple, squiggle, three, solid green, squiggle, two, striped green, oval, one, striped purple, oval, two, striped purple, oval, one, open red, squiggle, one, open green, squiggle, one, solid red, diamond, three, solid Set #1 green, diamond, one, open green, oval, one, striped green, squiggle, one, solid Set #2 green, diamond, one, open purple, oval, one, open red, squiggle, one, open Set #3 purple, squiggle, three, solid green, squiggle, two, striped red, squiggle, one, open Set #4 green, squiggle, two, striped purple, oval, one, open red, diamond, three, solid purple, squiggle, three, open red, oval, two, open purple, oval, two, solid green, squiggle, two, solid purple, diamond, two, striped purple, squiggle, two, solid green, oval, two, striped red, oval, one, striped red, squiggle, two, striped green, diamond, three, solid green, diamond, two, open purple, oval, one, open Set #1 red, oval, two, open purple, oval, two, solid green, oval, two, striped Set #2 red, oval, two, open green, squiggle, two, solid purple, diamond, two, striped Set #3 purple, oval, two, solid red, squiggle, two, striped green, diamond, two, open Set #4 green, squiggle, two, solid green, oval, two, striped green, diamond, two, open Set #5 purple, diamond, two, striped green, oval, two, striped red, squiggle, two, striped Set #6 red, squiggle, two, striped green, diamond, three, solid purple, oval, one, open ``` ## Perl {{transPerl6}} It's actually slightly simplified, since generating Enum classes and objects would be overkill for this particular task. ```perl #!perl use strict; use warnings; # This code was adapted from the perl6 solution for this task. # Each element of the deck is an integer, which, when written # in octal, has four digits, which are all either 1, 2, or 4. my $fmt = '%4o'; my @deck = grep sprintf($fmt, $_) !~ tr/124//c, 01111 .. 04444; # Given a feature digit (1, 2, or 4), produce the feature's name. # Note that digits 0 and 3 are unused. my @features = map [split ' '], split /\n/,<<''; ! red green ! purple ! one two ! three ! oval squiggle ! diamond ! solid open ! striped 81 == @deck or die "There are ".@deck." cards (should be 81)"; # By default, draw 9 cards, but if the user # supplied a parameter, use that. my $draw = shift(@ARGV)  9; my $goal = int($draw/2); # Get the possible combinations of 3 indices into $draw elements. my @combinations = combine(3, 0 .. $draw1); my @sets; do { # Shuffle the first $draw elements of @deck. for my $i ( 0 .. $draw1 ) { my $j = $i + int rand(@deck  $i); @deck[$i, $j] = @deck[$j, $i]; } # Find all valid sets using the shuffled elements. @sets = grep { my $or = 0; $or = $_ for @deck[@$_]; # If all colors (or whatever) are the same, then # a 1, 2, or 4 will result when we OR them together. # If they're all different, then a 7 will result. # If any other digit occurs, the set is invalid. sprintf($fmt, $or) !~ tr/1247//c; } @combinations; # Continue until there are exactly $goal valid sets. } until @sets == $goal; print "Drew $draw cards:\n"; for my $i ( 0 .. $#sets ) { print "Set ", $i+1, ":\n"; my @cards = @deck[ @{$sets[$i]} ]; for my $card ( @cards ) { my @octal = split //, sprintf '%4o', $card; my @f = map $features[$_][$octal[$_]], 0 .. 3; printf " %6s %5s %8s %s\n", @f; } } exit; # This function is adapted from the perl5i solution for the # RosettaCode Combinations task. sub combine { my $n = shift; return unless @_; return map [$_], @_ if $n == 1; my $head = shift; my @result = combine( $n1, @_ ); unshift @$_, $head for @result; @result, combine( $n, @_ ); } __END__ ``` {{out}} ```txt Drew 12 cards: Set 1: red three oval striped green three diamond striped purple three squiggle striped Set 2: red three oval striped purple three squiggle open green three diamond solid Set 3: purple one diamond striped red three diamond striped green two diamond striped Set 4: green three diamond striped green three diamond open green three diamond solid Set 5: red three diamond striped green three oval solid purple three squiggle open Set 6: green two diamond striped purple three squiggle striped red one oval striped ``` ## Perl 6 The trick here is to allocate three different bits for each enum, with the result that the cards of a matching set OR together to produce a 4digit octal number that contains only the digits 1, 2, 4, or 7. This OR is done by funny looking [+], which is the reduction form of +, which is the numeric bitwise OR. (Because Perl 6 stole the bare  operator for composing junctions instead.) ```perl6 enum Color (red => 0o1000, green => 0o2000, purple => 0o4000); enum Count (one => 0o100, two => 0o200, three => 0o400); enum Shape (oval => 0o10, squiggle => 0o20, diamond => 0o40); enum Style (solid => 0o1, open => 0o2, striped => 0o4); my @deck = Color.enums X Count.enums X Shape.enums X Style.enums; sub MAIN($DRAW = 9, $GOAL = $DRAW div 2) { sub showcards(@c) { { printf "%9s%7s%10s%9s\n", @c[$_;*]».key } for ^@c } my @combinations = [^$DRAW].combinations(3); my @draw; repeat until (my @sets) == $GOAL { @draw = @deck.pick($DRAW); my @bits = @draw.map: { [+] @^enums».value } @sets = gather for @combinations > @c { take @draw[@c].item when /^ <[1247]>+ $/ given ( [+] @bits[@c] ).base(8); } } say "Drew $DRAW cards:"; showcards @draw; for @sets.kv > $i, @cards { say "\nSet {$i+1}:"; showcards @cards; } } ``` {{out}} ```txt Drew 9 cards: purple two diamond open red two squiggle striped purple three squiggle open purple two squiggle striped red three oval striped red one diamond striped purple two oval solid green three diamond solid red two squiggle open Set 1: purple two diamond open purple two squiggle striped purple two oval solid Set 2: purple two diamond open red one diamond striped green three diamond solid Set 3: red two squiggle striped red three oval striped red one diamond striped Set 4: purple three squiggle open red three oval striped green three diamond solid ``` ## Phix Converts cards 1..81 (that idea from C) to 1/2/4 [/7] (that idea from Perl) but inverts the validation ```Phix function comb(sequence pool, integer needed, sequence res={}, integer done=0, sequence chosen={}) if needed=0 then  got a full set sequence {a,b,c} = chosen if not find_any({3,5,6},flatten(sq_or_bits(sq_or_bits(a,b),c))) then res = append(res,chosen) end if elsif done+needed<=length(pool) then  get all combinations with and without the next item: done += 1 res = comb(pool,needed1,res,done,append(chosen,pool[done])) res = comb(pool,needed,res,done,chosen) end if return res end function constant m124 = {1,2,4} function card(integer n) returns the nth card (n is 1..81, res is length 4 of 1/2/4) n = 1 sequence res = repeat(0,4) for i=1 to 4 do res[i] = m124[remainder(n,3)+1] n = floor(n/3) end for return res end function constant colours = {"red", "green", 0, "purple"}, symbols = {"oval", "squiggle", 0, "diamond"}, numbers = {"one", "two", 0, "three"}, shades = {"solid", "open", 0, "striped"} procedure print_cards(sequence hand, sequence cards) for i=1 to length(cards) do integer {c,m,n,g} = cards[i], id = find(cards[i],hand) printf(1,"%3d: %7s %9s %6s %s\n",{id,colours[c],symbols[m],numbers[n],shades[g]}) end for printf(1,"\n") end procedure procedure play(integer cards=9, integer sets=4) integer deals = 1 while 1 do sequence deck = shuffle(tagset(81)) sequence hand = deck[1..cards] for i=1 to length(hand) do hand[i] = card(hand[i]) end for sequence res = comb(hand,3) if length(res)=sets then printf(1,"dealt %d cards (%d deals)\n",{cards,deals}) print_cards(hand,hand) printf(1,"with %d sets\n",{sets}) for i=1 to sets do print_cards(hand,res[i]) end for exit end if deals += 1 end while end procedure play() play(12,6) play(9,6) ``` {{out}} ```txt dealt 9 cards (172 deals) 1: red oval two open 2: green oval one solid 3: purple diamond two striped 4: green diamond one striped 5: green oval one striped 6: purple squiggle three solid 7: green diamond two solid 8: red diamond two open 9: green squiggle one striped with 4 sets 1: red oval two open 4: green diamond one striped 6: purple squiggle three solid 3: purple diamond two striped 7: green diamond two solid 8: red diamond two open 4: green diamond one striped 5: green oval one striped 9: green squiggle one striped 5: green oval one striped 6: purple squiggle three solid 8: red diamond two open ``` ## Python ```python #!/usr/bin/python from itertools import product, combinations from random import sample ## Major constants features = [ 'green purple red'.split(), 'one two three'.split(), 'oval diamond squiggle'.split(), 'open striped solid'.split() ] deck = list(product(list(range(3)), repeat=4)) dealt = 9 ## Functions def printcard(card): print(' '.join('%8s' % f[i] for f,i in zip(features, card))) def getdeal(dealt=dealt): deal = sample(deck, dealt) return deal def getsets(deal): good_feature_count = set([1, 3]) sets = [ comb for comb in combinations(deal, 3) if all( [(len(set(feature)) in good_feature_count) for feature in zip(*comb)] ) ] return sets def printit(deal, sets): print('Dealt %i cards:' % len(deal)) for card in deal: printcard(card) print('\nFound %i sets:' % len(sets)) for s in sets: for card in s: printcard(card) print('') if __name__ == '__main__': while True: deal = getdeal() sets = getsets(deal) if len(sets) == dealt / 2: break printit(deal, sets) ``` Note: You could remove the inner square brackets of the 'if all( [...] )'
part of the sets computation in the getsets function. It is a remnant of Python 2.7 debugging which gives access to the namefeature
. The code works on Python 3.X too, but not that access. {{out}} ```txt Dealt 9 cards: green three squiggle solid green three squiggle open purple two squiggle solid green one diamond solid red three oval solid green two oval solid red two oval open purple one diamond striped red two oval solid Found 4 sets: green three squiggle solid green one diamond solid green two oval solid green three squiggle solid red two oval open purple one diamond striped green three squiggle open purple one diamond striped red two oval solid purple two squiggle solid green one diamond solid red three oval solid ``` ### Short Version {{transD}} ```python import random, pprint from itertools import product, combinations N_DRAW = 9 N_GOAL = N_DRAW // 2 deck = list(product("red green purple".split(), "one two three".split(), "oval squiggle diamond".split(), "solid open striped".split())) sets = [] while len(sets) != N_GOAL: draw = random.sample(deck, N_DRAW) sets = [cs for cs in combinations(draw, 3) if all(len(set(t)) in [1, 3] for t in zip(*cs))] print "Dealt %d cards:" % len(draw) pprint.pprint(draw) print "\nContaining %d sets:" % len(sets) pprint.pprint(sets) ``` {{out}} ```txt Dealt 9 cards: [('purple', 'three', 'squiggle', 'striped'), ('red', 'one', 'squiggle', 'solid'), ('red', 'three', 'diamond', 'striped'), ('red', 'two', 'oval', 'open'), ('purple', 'three', 'squiggle', 'open'), ('green', 'three', 'oval', 'open'), ('purple', 'three', 'squiggle', 'solid'), ('green', 'two', 'squiggle', 'open'), ('purple', 'two', 'oval', 'open')] Containing 4 sets: [(('purple', 'three', 'squiggle', 'striped'), ('red', 'one', 'squiggle', 'solid'), ('green', 'two', 'squiggle', 'open')), (('purple', 'three', 'squiggle', 'striped'), ('purple', 'three', 'squiggle', 'open'), ('purple', 'three', 'squiggle', 'solid')), (('red', 'one', 'squiggle', 'solid'), ('red', 'three', 'diamond', 'striped'), ('red', 'two', 'oval', 'open')), (('red', 'three', 'diamond', 'striped'), ('green', 'three', 'oval', 'open'), ('purple', 'three', 'squiggle', 'solid'))] ``` ## Racket ```Racket #lang racket (struct card [bits name]) (define cards (for/list ([C '(red green purple )] [Ci '(#o0001 #o0002 #o0004)] #:when #t [S '(oval squiggle diamond)] [Si '(#o0010 #o0020 #o0040)] #:when #t [N '(one two three )] [Ni '(#o0100 #o0200 #o0400)] #:when #t [D '(solid open striped)] [Di '(#o1000 #o2000 #o4000)]) (card (bitwiseior Ci Si Ni Di) (format "~a, ~a, ~a, ~a" C S N D)))) (define (nsubsets l n) (cond [(zero? n) '(())] [(null? l) '()] [else (append (for/list ([l2 (nsubsets (cdr l) ( n 1))]) (cons (car l) l2)) (nsubsets (cdr l) n))])) (define (set? cards) (regexpmatch? #rx"^[1247]*$" (number>string (apply bitwiseior (map cardbits cards)) 8))) (define (deal C S) (define hand (take (shuffle cards) C)) (define 3sets (filter set? (nsubsets hand 3))) (cond [(not (= S (length 3sets))) (deal C S)] [else (printf "Dealt ~a cards:\n" C) (for ([c hand]) (printf " ~a\n" (cardname c))) (printf "\nContaining ~a sets:\n" S) (for ([set 3sets]) (for ([c set]) (printf " ~a\n" (cardname c))) (newline))])) (deal 9 4) (deal 12 6) ``` ## REXX Language note: each REXX implementation has its own method of determining a starter ''seed'' for generating pseudorandom numbers, and in addition, that starter seed may be dependent upon operating system factors, hardware architecture, and other things like the (local) date and timeofday, and other such variables. The algorithm is also not the same for all REXX implementations. The particular set of cards dealt (show below) used Regina 3.90 under a Windows/XP environment. ```rexx /*REXX program finds "sets" (solutions) for the SET puzzle (game). */ parse arg game seed . /*get optional # cards to deal and seed*/ if game ==','  game=='' then game=9 /*Not specified? Then use the default.*/ if seed==','  seed=='' then seed=77 /* " " " " " " */ call aGame 0 /*with tell=0: suppress the output. */ call aGame 1 /*with tell=1: display " " */ exit sets /*stick a fork in it, we're all done. */ /*──────────────────────────────────AGAME subroutine──────────────────────────*/ aGame: tell=arg(1); good=game%2 /*enable/disable the showing of output.*/ /* [↑] the GOOD var is the right #sets*/ do seed=seed until good==sets /*generate deals until good # of sets.*/ call random ,,seed /*repeatability for the RANDOM invokes.*/ call genFeatures /*generate various card game features. */ call genDeck /*generate a deck (with 81 "cards").*/ call dealer game /*deal a number of cards for the game. */ call findSets game%2 /*find # of sets from the dealt cards. */ end /*until*/ /* [↓] when leaving, SETS is right #.*/ return /*return to invoker of this subroutine.*/ /*──────────────────────────────────DEALER subroutine─────────────────────────*/ dealer: call sey 'dealing' game "cards:",,. /*shuffle and deal the cards. */ do cards=1 until cards==game /*keep dealing until finished.*/ _=random(1,words(##)); ##=delword(##,_,1) /*pick card; delete a card. */ @.cards=deck._ /*add the card to the tableau.*/ call sey right('card' cards,30) " " @.cards /*display the card to screen. */ do j=1 for words(@.cards) /* [↓] define cells for cards*/ @.cards.j=word(@.cards,j) /*define a cell for a card.*/ end /*j*/ end /*cards*/ return /*──────────────────────────────────DEFFEATURES subroutine────────────────────*/ defFeatures: parse arg what,v; _=words(v) /*obtain what is to be defined*/ if _\==values then do; call sey 'error,' what "features ¬=" values,.,. exit 1 end /* [↑] check for typos/errors*/ do k=1 for words(values) /*define all the possible vals*/ call value what'.'k, word(values,k) /*define a card feature. */ end /*k*/ return /*──────────────────────────────────GENDECK subroutine────────────────────────*/ genDeck: #=0; ##= /*#: cards in deck; ##: shuffle aid.*/ do num=1 for values; xnum = word(numbers, num) do col=1 for values; xcol = word(colors, col) do sym=1 for values; xsym = word(symbols, sym) do sha=1 for values; xsha = word(shadings, sha) #=#+1; ##=## #; deck.#=xnum xcol xsym xsha /*create a card.*/ end /*sha*/ end /*num*/ end /*sym*/ end /*col*/ return /*#: the number of cards in the deck. */ /*──────────────────────────────────GENFEATURES subroutine────────────────────*/ genFeatures: features=3; groups=4; values=3 /*define # features, groups, vals.*/ numbers = 'one two three' ; call defFeatures 'number', numbers colors = 'red green purple' ; call defFeatures 'color', colors symbols = 'oval squiggle diamond' ; call defFeatures 'symbol', symbols shadings= 'solid open striped' ; call defFeatures 'shading', shadings return /*──────────────────────────────────GENPOSS subroutine────────────────────────*/ genPoss: p=0; sets=0; sep=' ───── '; !.= /*define some REXX variables. */ do i=1 for game /* [↓] the IFs eliminate duplicates.*/ do j=i+1 to game do k=j+1 to game p=p+1; [email protected]; [email protected]; [email protected] end /*k*/ end /*j*/ end /*i*/ /* [↑] generate the permutation list. */ return /*──────────────────────────────────FINDSETS subroutine───────────────────────*/ findSets: parse arg n; call genPoss /*N: the number of sets to be found. */ call sey /*find any sets that were generated [↑]*/ do j=1 for p /*P: is the number of possible sets. */ do f=1 for features do g=1 for groups; !!.j.f.g=word(!.j.f, g) end /*g*/ end /*f*/ ok=1 /*everything is peachy─kean (OK) so far*/ do g=1 for groups; _=!!.j.1.g /*build strings to hold possibilities. */ equ=1 /* [↓] handles all the equal features.*/ do f=2 to features while equ; equ=equ & _==!!.j.f.g end /*f*/ dif=1 __=!!.j.1.g /* [↓] handles all unequal features.*/ do f=2 to features while \equ dif=dif & (wordpos(!!.j.f.g,__)==0) __=__ !!.j.f.g /*append to the string for next test. */ end /*f*/ ok=ok & (equ  dif) /*now, see if all are equal or unequal.*/ end /*g*/ if \ok then iterate /*Is this set OK? Nope, then skip it.*/ sets=sets+1 /*bump the number of the sets found. */ call sey right('set' sets": ",15) !.j.1 sep !.j.2 sep !.j.3 end /*j*/ call sey sets 'sets found.',. return /*──────────────────────────────────SEY subroutine────────────────────────────*/ sey: if \tell then return /*¬ tell? Then suppress the output. */ if arg(2)==. then say; say arg(1); if arg(3)==. then say; return ``` '''output''' when using the default input: ```txt dealing 9 cards: card 1 one green oval open card 2 two purple squiggle striped card 3 one green diamond solid card 4 three red diamond open card 5 two purple squiggle striped card 6 two purple oval striped card 7 two purple diamond striped card 8 three red squiggle open card 9 two red oval solid set 1: two purple squiggle striped ───── two purple oval striped ───── two purple diamond striped set 2: one green diamond solid ───── three red diamond open ───── two purple diamond striped set 3: one green diamond solid ───── two purple oval striped ───── three red squiggle open set 4: two purple squiggle striped ───── two purple oval striped ───── two purple diamond striped 4 sets found. ``` '''output''' when using the input of: 12 ```txt dealing 12 cards: card 1 one purple diamond striped card 2 one green diamond striped card 3 one purple squiggle solid card 4 one red oval solid card 5 two green oval open card 6 one green diamond open card 7 two green squiggle striped card 8 three green squiggle solid card 9 three green squiggle open card 10 one purple diamond open card 11 three green squiggle open card 12 two red oval open set 1: one purple diamond striped ───── three green squiggle solid ───── two red oval open set 2: one green diamond striped ───── two green oval open ───── three green squiggle solid set 3: two green oval open ───── one green diamond open ───── three green squiggle open set 4: two green oval open ───── one green diamond open ───── three green squiggle open set 5: three green squiggle open ───── one purple diamond open ───── two red oval open set 6: one purple diamond open ───── three green squiggle open ───── two red oval open 6 sets found. ``` ## Ruby Brute force. ```ruby COLORS = %i(red green purple) #use [:red, :green, :purple] in Ruby < 2.0 SYMBOLS = %i(oval squiggle diamond) NUMBERS = %i(one two three) SHADINGS = %i(solid open striped) DECK = COLORS.product(SYMBOLS, NUMBERS, SHADINGS) def get_all_sets(hand) hand.combination(3).select do candidate grouped_features = candidate.flatten.group_by{f f} grouped_features.values.none?{v v.size == 2} end end def get_puzzle_and_answer(hand_size, num_sets_goal) begin hand = DECK.sample(hand_size) sets = get_all_sets(hand) end until sets.size == num_sets_goal [hand, sets] end def print_cards(cards) puts cards.map{card " %8s" * 4 % card} puts end def set_puzzle(deal, goal=deal/2) puzzle, sets = get_puzzle_and_answer(deal, goal) puts "Dealt #{puzzle.size} cards:" print_cards(puzzle) puts "Containing #{sets.size} sets:" sets.each{set print_cards(set)} end set_puzzle(9) set_puzzle(12) ``` {{out}} ```txt Dealt 9 cards: red diamond two open red squiggle three open red diamond two striped red diamond two solid red oval three striped green squiggle three open red oval three open red squiggle one striped red oval one open Containing 4 sets: red diamond two open red squiggle three open red oval one open red diamond two open red diamond two striped red diamond two solid red diamond two striped red oval three striped red squiggle one striped red diamond two solid red oval three open red squiggle one striped Dealt 12 cards: red diamond three solid red diamond three striped purple squiggle one striped purple oval two striped green diamond two open purple oval three open red diamond one striped green oval one solid purple squiggle two solid green oval two open red oval two striped red diamond two striped Containing 6 sets: red diamond three solid purple squiggle one striped green oval two open red diamond three solid green oval one solid purple squiggle two solid red diamond three striped red diamond one striped red diamond two striped green diamond two open purple squiggle two solid red oval two striped purple oval three open green oval one solid red oval two striped purple squiggle two solid green oval two open red diamond two striped ``` ## Tcl The principle behind this code is that the space of possible solutions is a substantial proportion of the space of possible hands, so picking a random hand and verifying that it is a solution, repeating until that verification succeeds, is a much quicker way to find a solution than a systematic search. It also makes the code substantially simpler. ```tcl # Generate random integer uniformly on range [0..$n1] proc random n {expr {int(rand() * $n)}} # Generate a shuffled deck of all cards; the card encoding was stolen from the # Perl6 solution. This is done once and then used as a constant. Note that the # rest of the code assumes that all cards in the deck are unique. set ::AllCards [apply {{} { set cards {} foreach color {1 2 4} { foreach symbol {1 2 4} { foreach number {1 2 4} { foreach shading {1 2 4} { lappend cards [list $color $symbol $number $shading] } } } } # KnuthMorrisPratt shuffle (not that it matters) for {set i [llength $cards]} {$i > 0} {} { set j [random $i] set tmp [lindex $cards [incr i 1]] lset cards $i [lindex $cards $j] lset cards $j $tmp } return $cards }}] # Randomly pick a hand of cards from the deck (itself in a global for # convenience). proc drawCards n { set cards $::AllCards; # Copies... for {set i 0} {$i < $n} {incr i} { set idx [random [llength $cards]] lappend hand [lindex $cards $idx] set cards [lreplace $cards $idx $idx] } return $hand } # Test if a particular group of three cards is a valid set proc isValidSet {a b c} { expr { ([lindex $a 0][lindex $b 0][lindex $c 0]) in {1 2 4 7} && ([lindex $a 1][lindex $b 1][lindex $c 1]) in {1 2 4 7} && ([lindex $a 2][lindex $b 2][lindex $c 2]) in {1 2 4 7} && ([lindex $a 3][lindex $b 3][lindex $c 3]) in {1 2 4 7} } } # Get all unique valid sets of three cards in a hand. proc allValidSets {hand} { set sets {} for {set i 0} {$i < [llength $hand]} {incr i} { set a [lindex $hand $i] set hand [set cards2 [lreplace $hand $i $i]] for {set j 0} {$j < [llength $cards2]} {incr j} { set b [lindex $cards2 $j] set cards2 [set cards3 [lreplace $cards2 $j $j]] foreach c $cards3 { if {[isValidSet $a $b $c]} { lappend sets [list $a $b $c] } } } } return $sets } # Solve a particular version of the set puzzle, by picking random hands until # one is found that satisfies the constraints. This is usually much faster # than a systematic search. On success, returns the hand found and the card # sets within that hand. proc SetPuzzle {numCards numSets} { while 1 { set hand [drawCards $numCards] set sets [allValidSets $hand] if {[llength $sets] == $numSets} { break } } return [list $hand $sets] } ``` Demonstrating: ```tcl # Render a hand (or any list) of cards (the "."s are just placeholders). proc PrettyHand {hand {separator \n}} { set Co {. red green . purple} set Sy {. oval squiggle . diamond} set Nu {. one two . three} set Sh {. solid open . striped} foreach card $hand { lassign $card co s n sh lappend result [format "(%s,%s,%s,%s)" \ [lindex $Co $co] [lindex $Sy $s] [lindex $Nu $n] [lindex $Sh $sh]] } return $separator[join $result $separator] } # Render the output of the Set Puzzle solver. proc PrettyOutput {setResult} { lassign $setResult hand sets set sep "\n " puts "Hand (with [llength $hand] cards) was:[PrettyHand $hand $sep]" foreach s $sets { puts "Found set [incr n]:[PrettyHand $s $sep]" } } # Demonstrate on the two cases puts " ### BASIC PUZZLE ====== " PrettyOutput [SetPuzzle 9 4] puts " ### ADVANCED PUZZLE === " PrettyOutput [SetPuzzle 12 6] ``` {{outSample output}} ```txt ### BASIC PUZZLE ====== Hand (with 9 cards) was: (purple,squiggle,one,solid) (green,diamond,two,striped) (green,oval,two,striped) (purple,diamond,three,striped) (red,oval,three,open) (green,squiggle,three,solid) (red,squiggle,one,solid) (red,oval,one,solid) (purple,oval,three,open) Found set 1: (purple,squiggle,one,solid) (green,diamond,two,striped) (red,oval,three,open) Found set 2: (green,oval,two,striped) (purple,oval,three,open) (red,oval,one,solid) Found set 3: (red,oval,three,open) (green,squiggle,three,solid) (purple,diamond,three,striped) Found set 4: (red,squiggle,one,solid) (green,diamond,two,striped) (purple,oval,three,open) ### ADVANCED PUZZLE === Hand (with 12 cards) was: (green,diamond,two,open) (red,diamond,one,solid) (purple,diamond,one,solid) (red,squiggle,two,open) (green,diamond,three,open) (red,oval,two,striped) (red,diamond,two,solid) (purple,diamond,two,striped) (purple,diamond,three,open) (purple,diamond,three,striped) (purple,oval,three,open) (purple,squiggle,two,striped) Found set 1: (green,diamond,two,open) (red,diamond,one,solid) (purple,diamond,three,striped) Found set 2: (green,diamond,two,open) (purple,diamond,two,striped) (red,diamond,two,solid) Found set 3: (purple,diamond,one,solid) (purple,diamond,three,open) (purple,diamond,two,striped) Found set 4: (purple,diamond,one,solid) (purple,oval,three,open) (purple,squiggle,two,striped) Found set 5: (green,diamond,three,open) (red,diamond,one,solid) (purple,diamond,two,striped) Found set 6: (red,diamond,two,solid) (red,oval,two,striped) (red,squiggle,two,open) ``` ## zkl {{transD}} ```zkl const nDraw=9, nGoal=(nDraw/2); // Basic var [const] UH=Utils.Helpers; // baked in stash of goodies deck:=Walker.cproduct("red green purple".split(), // Cartesian product of 4 lists of lists "one two three".split(), // T(1,2,3) (ie numbers) also works "oval squiggle diamond".split(), "solid open striped".split()).walk(); reg draw,sets,N=0; do{ N+=1; draw=deck.shuffle()[0,nDraw]; // one draw per shuffle sets=UH.pickNFrom(3,draw) // 84 sets of 3 cards (each with 4 features) .filter(fcn(set){ // list of 12 items (== 3 cards) set[0,4].zip(set[4,4],set[8,4]) // >4 tuples of 3 features .pump(List,UH.listUnique,"len", // 1,3 (good) or 2 (bad) '==(2)) // (F,F,F,F)==good .sum(0) == 0 // all 4 feature sets good }); }while(sets.len()!=nGoal); println("Dealt %d cards %d times:".fmt(draw.len(),N)); draw.pump(Void,fcn(card){ println(("%8s "*4).fmt(card.xplode())) }); println("\nContaining:"); sets.pump(Void,fcn(card){ println((("%8s "*4 + "\n")*3).fmt(card.xplode())) }); ``` {{out}} ```txt Dealt 9 cards 271 times: red one oval solid green one diamond striped red two oval open purple two squiggle striped green three diamond open purple three squiggle solid purple one diamond striped green three squiggle solid green one squiggle open Containing: red one oval solid purple two squiggle striped green three diamond open red one oval solid purple one diamond striped green one squiggle open green one diamond striped red two oval open purple three squiggle solid red two oval open purple one diamond striped green three squiggle solid ```