Are you a professional problem solver? If so, we invite you to submit your “Ponder This” solution for this month’s challenge. **Ponder This** is IBM Research’s monthly brain-twister where you can match wits with some of the best minds at IBM.

**Ponder This Challenge: **

This month’s challenge is from Thomas Dueholm Hansen and Uri Zwick (thanks).

Find a matrix of bits T which has at least 21 rows and 6 columns such that the following holds:

1) For every row 1<=i_1<21 there exists a column j such that T(i_1,j) != T(i_1+1,j) and T(i_1+1,j) = T(21,j)

2) For every pair of rows 1<=i_1< i_2<21 there exists a column j such that T(i_1,j) != T(i_1+1,j) and T(i_1+1,j) = T(i_2,j) = T(i_2+1,j).

Here is an example of a solution for the same problem with an 8 x 4 matrix:

0011

1101

1010

1100

0110

0100

0000

0001

Bonus question: Find this type of matrix with at least 33 rows and 7 columns.

________

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*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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