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=Optimal solution in 52 single moves:=
15 14 1 6 9 11 4 12 0 10 7 3 13 8 5 2
15 14 1 6 9 11 4 12 10 0 7 3 13 8 5 2
15 14 1 6 9 11 4 12 10 7 0 3 13 8 5 2
15 14 1 6 9 11 4 12 10 7 3 0 13 8 5 2
15 14 1 6 9 11 4 0 10 7 3 12 13 8 5 2
15 14 1 6 9 11 0 4 10 7 3 12 13 8 5 2
15 14 1 6 9 11 3 4 10 7 0 12 13 8 5 2
15 14 1 6 9 11 3 4 10 7 5 12 13 8 0 2
15 14 1 6 9 11 3 4 10 7 5 12 13 0 8 2
15 14 1 6 9 11 3 4 10 0 5 12 13 7 8 2
15 14 1 6 9 0 3 4 10 11 5 12 13 7 8 2
15 0 1 6 9 14 3 4 10 11 5 12 13 7 8 2
0 15 1 6 9 14 3 4 10 11 5 12 13 7 8 2
9 15 1 6 0 14 3 4 10 11 5 12 13 7 8 2
9 15 1 6 14 0 3 4 10 11 5 12 13 7 8 2
9 0 1 6 14 15 3 4 10 11 5 12 13 7 8 2
9 1 0 6 14 15 3 4 10 11 5 12 13 7 8 2
9 1 3 6 14 15 0 4 10 11 5 12 13 7 8 2
9 1 3 6 14 15 5 4 10 11 0 12 13 7 8 2
9 1 3 6 14 15 5 4 10 11 8 12 13 7 0 2
9 1 3 6 14 15 5 4 10 11 8 12 13 7 2 0
9 1 3 6 14 15 5 4 10 11 8 0 13 7 2 12
9 1 3 6 14 15 5 4 10 11 0 8 13 7 2 12
9 1 3 6 14 15 5 4 10 0 11 8 13 7 2 12
9 1 3 6 14 0 5 4 10 15 11 8 13 7 2 12
9 1 3 6 0 14 5 4 10 15 11 8 13 7 2 12
0 1 3 6 9 14 5 4 10 15 11 8 13 7 2 12
1 0 3 6 9 14 5 4 10 15 11 8 13 7 2 12
1 3 0 6 9 14 5 4 10 15 11 8 13 7 2 12
1 3 6 0 9 14 5 4 10 15 11 8 13 7 2 12
1 3 6 4 9 14 5 0 10 15 11 8 13 7 2 12
1 3 6 4 9 14 5 8 10 15 11 0 13 7 2 12
1 3 6 4 9 14 5 8 10 15 0 11 13 7 2 12
1 3 6 4 9 14 5 8 10 15 2 11 13 7 0 12
1 3 6 4 9 14 5 8 10 15 2 11 13 0 7 12
1 3 6 4 9 14 5 8 10 0 2 11 13 15 7 12
1 3 6 4 9 0 5 8 10 14 2 11 13 15 7 12
1 3 6 4 9 5 0 8 10 14 2 11 13 15 7 12
1 3 6 4 9 5 2 8 10 14 0 11 13 15 7 12
1 3 6 4 9 5 2 8 10 14 7 11 13 15 0 12
1 3 6 4 9 5 2 8 10 14 7 11 13 0 15 12
1 3 6 4 9 5 2 8 10 0 7 11 13 14 15 12
1 3 6 4 9 5 2 8 0 10 7 11 13 14 15 12
1 3 6 4 0 5 2 8 9 10 7 11 13 14 15 12
1 3 6 4 5 0 2 8 9 10 7 11 13 14 15 12
1 3 6 4 5 2 0 8 9 10 7 11 13 14 15 12
1 3 0 4 5 2 6 8 9 10 7 11 13 14 15 12
1 0 3 4 5 2 6 8 9 10 7 11 13 14 15 12
1 2 3 4 5 0 6 8 9 10 7 11 13 14 15 12
1 2 3 4 5 6 0 8 9 10 7 11 13 14 15 12
1 2 3 4 5 6 7 8 9 10 0 11 13 14 15 12
1 2 3 4 5 6 7 8 9 10 11 0 13 14 15 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 =Optimal solution in 31 multi moves: u2r2d3ru2ld2ru3ld3l2u3r2d2l2dru3rd3l2u2r3dl3dru2r2d2=
original: move 1:u2 move 2:r2 move 3:d3 move 4:r move 5:u2 move 6:l move 7:d2
15 14 1 6 14 1 6 14 1 6 14 1 4 6 14 1 4 6 14 1 4 6 14 1 4 6 14 1 4 6
9 11 4 12 15 11 4 12 15 11 4 12 15 11 7 12 15 11 7 12 15 11 7 15 11 7 15 11 5 7
10 7 3 9 10 7 3 9 10 7 3 9 10 5 3 9 10 5 3 9 10 5 12 9 10 5 12 9 10 2 12
13 8 5 2 13 8 5 2 13 8 5 2 13 8 2 13 8 2 13 8 2 3 13 8 2 3 13 8 3
move 8:r move 9:u3 move 10:l move 11:d3 move 12:l2 move 13:u3 move 14:r2 move 15:d2
14 1 4 6 14 1 4 14 1 4 14 1 5 4 14 1 5 4 1 5 4 1 5 4 1 5 2 4
15 11 5 7 15 11 5 6 15 11 5 6 15 11 2 6 15 11 2 6 14 11 2 6 14 11 2 6 14 11 3 6
9 10 2 12 9 10 2 7 9 10 2 7 9 10 3 7 9 10 3 7 15 10 3 7 15 10 3 7 15 10 7
13 8 3 13 8 3 12 13 8 3 12 13 8 12 13 8 12 9 13 8 12 9 13 8 12 9 13 8 12
move 16:l2 move 17:d move 18:r move 19:u3 move 20:r move 21:d3 move 22:l2 move 23:u2
1 5 2 4 1 5 2 4 1 5 2 4 1 2 4 1 2 4 1 2 3 4 1 2 3 4 1 2 3 4
14 11 3 6 14 11 3 6 14 11 3 6 14 5 3 6 14 5 3 6 14 5 10 6 14 5 10 6 5 10 6
15 10 7 9 15 10 7 9 15 10 7 9 11 10 7 9 11 10 7 9 11 8 7 9 11 8 7 14 11 8 7
9 13 8 12 13 8 12 13 8 12 13 15 8 12 13 15 8 12 13 15 12 13 15 12 9 13 15 12
move 24:r3 move 25:d move 26:l3 move 27:d move 28:r move 29:u2 move 30:r2 move 31:d2
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
5 10 6 5 10 6 7 5 10 6 7 5 10 6 7 5 10 6 7 5 6 7 5 6 7 5 6 7 8
14 11 8 7 14 11 8 14 11 8 9 14 11 8 9 14 11 8 9 10 11 8 9 10 11 8 9 10 11 12
9 13 15 12 9 13 15 12 9 13 15 12 13 15 12 13 15 12 13 14 15 12 13 14 15 12 13 14 15