This month’s challenge is from Thomas Dueholm Hansen and Uri Zwick(thanks).Find a matrix of bits T which has 6 columns and at least 21 rows such thatthe following holds:

1) For every row 1 <= i1 < 21 there exists a column j such that T (i1, j)! =T (i1 + 1, j) and T (i1 + 1, j) = T (21, j)

2) For every pair of rows 1 <= i1 < i2 < 21 there exists a column j suchthat T (i1, j)! = T (i1 + 1, j) and T (i1 + 1, j) = T (i2, j) = T (i2 + 1, j).

Here is an example of a solution for the same problem with an 8× 4 matrix:00111101101011000110010000000001Bonus question: Find this type of matrix with 7 columns and at least 33rows.

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