IBM Ponder This #200 · December 2014

Given an NxM binary matrix, we can compute the N sums of the rows and the M sums of the columns . These sums can sometimes uniquely define the matrix. For example, the sums [1,2,0][2,1] can be generated only from the matrix

1 0
1 1
0 0

But sometimes there are several options. For example [1,1,2][2,2] can be generated from two matrices:

0 1    1 0
1 0    0 1
1 1    1 1

The challenge this month is to find sums that are generated from exactly 29 different binary matrices.

To rule out trivial solution, we further require that each matrix have no more than 50 bits.

Please provide your answer as two lines, the first line with N integers and the second with M integers. N*M should be no more than 50.

Solution

Best opened after a real attempt

To be added.