KöMaL 2025 B5448

We have two congruent regular $n$-gon based pyramids. On the lateral faces of both pyramids, the numbers $1$, $2$, $\ldots$, $n$ are written in a random order. For which values of $n$ is it guaranteed that the bases of the pyramids can always be glued together in such a way that at least two edges of the resulting bipyramid satisfy the property that the two numbers on either side of the edges are equal to each other?