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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04487 |
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Table of Contents:
- We generalize the classical "1089-number trick", which states that a certain combination of addition, subtraction and swapping the digits of a three-digit number will always output 1089. More precisely, we show that any pair of zero divisors $fg=0$ in the group ring ${\mathbb Z}[Σ_n]$ on the n-th symmetric group gives rise to a partition of the set of n-digit numbers into subsets $U_{\mathbf e}$ defined by linear inequalities, such that the zero divisors act constantly on each $U_{\mathbf e}$ and hence define a number trick.