December 2014
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The trivial solution for any number N is [1,1,1,...,1][1,N-1], which gives a 56-bit matrix in our case (N=29). To disallow this solution, we required that the matrix have no more than 50 bits.
The second systematic way is [M-1,1,1,1,...,1][N-1,1,1,1,...,1], which generates 1+(N-1)*(M-1) matrices. This gives solutions like [7,1,1,1,1][4,1,1,1,1,1,1,1].
Gyorgy Gyomai sent us another way to generate a set of numbers: [M-1,2,1][2,2,1,1,1,...,1], which gives 3*k-4 different generating matrices, giving the solution [10,2,1],[2,2,1,1,1,1,1,1,1,1,1].
The smallest solution (24 bits) is [1,2,3,5],[1,1,1,2,3,3].
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com