Kati cut two equal regular $ n-gons$ out of paper. To the vertices of both $ n-gons$, she wrote the numbers 1 to $ n$ in some order. Then she stabbed a needle through the centres of these $ n-gons$ so that they could be rotated with respect to each other. Kati noticed that there is a position where the numbers at each pair of aligned vertices are different. Prove that the $ n-gons$ can be rotated to a position where at least two pairs of aligned vertices contain equal numbers.