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0 or 1 inside 2009 boxes Puerto Rico Ibero IMO TST 2009.2

Source:

September 16, 2021
combinatoricsconsecutive integersSum1434

Problem Statement

In each box of a 1×2009 1 \times 2009 grid, we place either a 0 0 or a 1 1, such that the sum of any 90 90 consecutive boxes is 65 65. Determine all possible values of the sum of the 2009 2009 boxes in the grid.
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