A proof of the Kikuta-Ruckle conjecture on cyclic caching of resources (Q438788)

The authors establish a conjecture which arose from work on accumulation games by Kikuta and Ruckle. They consider the problem of how a hider should distribute a continuously divisible good of mass \(y>1\) over a finite number of \(N\) locations, to maximize the probability that a critical amount remains, after an antagonostic searcher remove the material from \(N-k\) of these locations. This critical face defined by other components. They show that there exists an optimal resource distribution, which uses a finite number of point caches of equal size, establishing a conjecture of Kikuta and Ruckle.