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no 2, 3, 4, 5 in squares of 5x5 board , 2018 May Olympiad L1 p5

Source:

August 24, 2021
combinatorics

Problem Statement

In each square of a 5×55 \times 5 board one of the numbers 2,3,42, 3, 4 or 55 is written so that the the sum of all the numbers in each row, in each column and on each diagonal is always even. How many ways can we fill the board?
Clarification. A 5×55\times 5 board has exactly 1818 diagonals of different sizes. In particular, the corners are size 1 1 diagonals.
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