MathDB

25

Part of 2013 Stanford Mathematics Tournament

Problems(1)

2013 General Problem 25

Source:

2/4/2013
A 3×63\times 6 grid is filled with the numbers in the list {1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9}\{1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9\} according to the following rules: (1) Both the first three columns and the last three columns contain the integers 1 through 9. (2) No numbers appear more than once in a given row. Let NN be the number of ways to fill the grid and let kk be the largest positive integer such that 2k2^k divides NN. What is k?