IBM Research | Ponder This | January 2014 solutions
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January 2014

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One can solve this problem by either encoding it as a CNF formula and using any SAT solver, or running backtracking from the bottom of the table T.
Here are solutions for 21x6
000000
111111
100000
111110
010000
111100
001001
001110
010100
001101
100100
101101
110101
000111
110111
100011
110011
111011
111010
011010
011000
and for the bonus 33x7
0000000
1111111
1000000
1110111
0100000
1101111
0000010
1110011
1101000
0111011
1001001
0110001
1000101
0010001
1011101
0011000
1011110
1110000
1010110
1110100
0011100
0110101
0001101
0111101
0101100
0100111
0101101
0101111
0101010
1101011
1101010
1111010
1111110

The best solutions are
2x1
3x2
5x3
8x4
13x5
21x6

Bonus question: Can you find a 34x7 solution and keep the Fibonacci sequence?


If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com