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Write 1 or -1 on 2007x2007

Source: turkey 2007 TST

April 10, 2007
linear algebramatrixLaTeXinductionabsolute valuecombinatorics proposedcombinatorics

Problem Statement

We write 11 or −1-1 on each unit square of a 2007×20072007 \times 2007 board. Find the number of writings such that for every square on the board the absolute value of the sum of numbers on the square is less then or equal to 11.
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