1990 OIM Problems/Problem 5

Revision as of 12:44, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>A</math> and <math>B</math> be opposite vertices of a gridded board of <math>n</math> by <math>n</math> squares <math>n \ge 1</math>, to each of which...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $A$ and $B$ be opposite vertices of a gridded board of $n$ by $n$ squares $n \ge 1$, to each of which its diagonal of direction $AB$ is added, thus forming $2n^2$ equal triangles. A piece is moved along a path that goes from $A$ to $B$ formed by segments of the board, and each time it is traveled, a seed is placed in each of the triangles that accepts that segment as a side. The path is traveled in such a way that no segment is passed more than once, and it is observed, after traveling, that there are exactly two seeds in each of the $2n^2$ triangles of the board. For what values of $n$ is this situation possible?

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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://www.oma.org.ar/enunciados/ibe5.htm