2025/08/31 by Håkon Kolderup, Kolderup, Håkon
#FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2509.04487
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[Σn] 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.