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2020 Cono Sur Math Olympiad P6

Source: Cono Sur Math Olympiad 2020

December 4, 2020
combinatorics

Problem Statement

A 44 x 44 square board is called brasucabrasuca if it follows all the conditions:
• each box contains one of the numbers 0,1,2,3,40, 1, 2, 3, 4 or 55; • the sum of the numbers in each line is 55; • the sum of the numbers in each column is 55; • the sum of the numbers on each diagonal of four squares is 55; • the number written in the upper left box of the board is less than or equal to the other numbers the board; • when dividing the board into four 22 × 22 squares, in each of them the sum of the four numbers is 55.
How many "brasucas""brasucas" boards are there?
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