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1996 OIM Problems/Problem 3

Revision as of 15:04, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == We have a board of <math>k^2-k+1</math> rows and <math>k^2-k+1</math> columns, where <math>k=p+1</math> and <math>p</math> is a prime number. For each prime <mat...")
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Problem

We have a board of $k^2-k+1$ rows and $k^2-k+1$ columns, where $k=p+1$ and $p$ is a prime number. For each prime $p$, provide a method for distributing numbers 0 and 1, a number in each square of the board, so that in each row there are exactly $k$ numbers 0 and also there are no rectangles with parallel sides on the sides of the board with numbers 0 in its four vertices.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe11.htm

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