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2023 Fall Speed p4

Source:

December 23, 2023
2023FAlLspeedCombo

Problem Statement

The numbers 11, 22, 33, and 44 are randomly arranged in a 22 by 22 grid with one number in each cell. Find the probability the sum of two numbers in the top row of the grid is even.
Proposed by Muztaba Syed and Derek Zhao
Solution. 13\boxed{\dfrac{1}{3}} Pick a number for the top-left. There is one number that makes the sum even no matter what we pick. Therefore, the answer is 13\boxed{\dfrac{1}{3}}.
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