Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2310.13777 |
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Inhaltsangabe:
- We investigate a discrete search game called the Multiple Caching Game where the searcher's aim is to find all of a set of $d$ treasures hidden in $n$ locations. Allowed queries are sets of locations of size $k$, and the searcher wins if in all $d$ queries, at least one treasure is hidden in one of the $k$ picked locations. Pálvölgyi showed that the value of the game is at most $\frac{k^d}{\binom{n+d-1}{d}}$, with equality for large enough $n$. We conjecture the exact cases of equality. We also investigate variants of the game and show an example where their values are different, answering a question of Pálvölgyi. This game is closely related to a continuous variant, Alpern's Caching Game, based on which we define other continous variants of the multiple caching game and examine their values.