A symmetry approach to number tricks
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917383348682752 |
|---|---|
| author | Kolderup, Håkon |
| author_facet | Kolderup, Håkon |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A symmetry approach to number tricks Kolderup, Håkon General Mathematics 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. |
| title | A symmetry approach to number tricks |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2509.04487 |