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Ivaylo Kortezov
Bulgarian Academy of Sciences
https://doi.org/10.53656/math2021-2-8-aco
Abstract. In some regions of Bulgaria (at least) there is an Easter tradition, according to which in group of people first each one chooses a differently coloured egg, then each pair of people performs a swap (or swaps) by exchanging the eggs they currently have until everyone gets the originally chosen egg. This generates a natural question: if there are n people in the group, find the least number E(n) of swaps which makes this possible. We prove that E(n) is the least even number not less than n(n−1)/2. The sequence thus generated was added to the Online Encyclopedia of Integer Sequences and linked from there to several seemingly distant combinatorial results.
Keywords: combinatorics; swap; inversion; invariant; paths in a lattice
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