**Welcome 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.