2008 iTest Problems/Problem 51
Problem
Alexis imagines a grid of integers arranged sequentially in the following way:
She picks one number from each row so that no two numbers she picks are in the same column. She them proceeds to add them together and finds that is the sum. Next, she picks of the numbers that are distinct from the she picked the first time. Again she picks exactly one number from each row and column, and again the sum of all numbers is . Find the remainder when is divided by .
Solution
Notice that all the numbers of the first column are congruent to modulo , all of the numbers in the second column are congruent to modulo , and so on. That means the sum of Alexis's numbers is congruent to modulo . After calculating the sum and dividing by , we find that , so the remainder when is divided by is .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 50 |
Followed by: Problem 52 | |
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