MathDB

Let's call a checkered polygon a strip, which can be traversed entirely, starting from some of its cells and then moving only in two directions - up or to the right. Several such strips can be inserted into each other by shifting by a vector

(-1.1)

. Prove that for any strip consisting of an even number of cells, there is such an odd

k

that if you combine

k

of the same strips by inserting them sequentially into each other, then the resulting polygon can be divided along the grid lines into two equal parts. Proposed by I. Markelov, S. Markelov

Problem Statement