## Diffy naive

A week or so ago Rob Eastaway posted about the game Diffy on Twitter. Diffy begins with four numbers arranged around a cycle. Taking the (absolute values of) differences between adjacent pairs produces four more numbers around a cycle. If you start with positive integers then iterating this process eventually reaches . How many iterations …

## The Namer-Claimer game, part 2

Discrete Mathematics, Volume 344, Issue 3, March 2021, 112256 https://doi.org/10.1016/j.disc.2020.112256 arXiv I’ve previously written about the Namer-Claimer game.  I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound.  The upper bound makes use of randomness, but in a very controlled way.  Analysing a truly …

## The Namer-Claimer game

Consider the following game played on the integers from to .  In each round Namer names a forbidden distance , then Claimer claims a subset of that does not contain any two integers at distance .  After finitely many rounds, Claimer will have claimed sets that cover the whole of , at which point the …