Gespeichert in:
| Hauptverfasser: | , , , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1811.07451 |
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Inhaltsangabe:
- An ordered triple $(s,p,n)$ is called admissible if there exist two different multisets $X=\{x_1,x_2,\dotsc,x_n\}$ and $Y=\{y_1,y_2,\dotsc,y_n\}$ such that $X$ and $Y$ share the same sum $s$, the same product $p$, and the same size $n$. We first count the number of $n$ such that $(s,p,n)$ are admissible for a fixed $s$. We also fully characterize the values $p$ such that $(s,p,n)$ is admissible. Finally, we consider the situation where $r$ different multisets are needed, instead of just two. This project is also related to John Conway's wizard puzzle from the 1960s.