Ponder This — December’s Challenge!

SP-ponderthisWelcome to our monthly puzzles

You are cordially invited to match wits with some of the best minds in IBM Research. We’ll post a new one every month, and allow a month for you to submit solutions to the webmaster. We usually won’t reply individually to submitted solutions but every few days we will update a list of people who answered correctly. At the beginning of the next month, we’ll post the answer.

Here is the solution for our November 2014 problem.
And now… here’s our December challenge!

So give your mind a break from its routine—you never know what other problems you may solve in the process!

Ponder This Challenge:

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.

IBM Research will post the names of those who submit a correct, original solution to their website! If you don’t want your name posted then please include such a statement in your submission!  Please send your submission to the webmaster.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

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