MathDB

Let

n\geqslant 2

be an integer. A Welsh darts board is a disc divided into

2n

equal sectors, half of them being red and the other half being white. Two Welsh darts boards are matched if they have the same radius and they are superimposed so that each sector of the first board comes exactly over a sector of the second board.
Suppose that two given Welsh darts boards can be matched so that more than half of the paurs of superimposed sectors have different colours. Prove that these Welsh darts boards can be matched so that at least

2\lfloor n/2\rfloor +2

pairs of superimposed sectors have the same colour.

Problem Statement