December 2012
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There are several ways to solve this month's challenge. One method is to start with an all-1 matrix, incrementing random places as long as the result satisfies the rules. Restart when you are stuck and after a while you'll get a solution.
Another way is to encode the challenge as an optimization problem and solve it using a SAT solver, BDD, CP, or MILP. Some of the solvers can do it in seconds.
We also received correct solutions that were achieved using manual trial-and-error on an MS-Excel worksheet.
Deron Stewart was the first to send a solution without 5:
2 4 1 4 2 1
1 3 2 3 4 1
2 4 4 1 4 2
4 1 3 2 3 4
3 2 4 4 1 1
1 3 1 3 2 3
Mark Mammel was the first to send an optimal solution of 93:
1 3 2 3 1 3
2 5 1 4 5 2
3 4 1 2 3 1
1 2 3 5 4 1
3 5 4 1 2 3
2 1 2 3 4 1
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com