Math riddle that 4 of us can't solve.

Question

The riddle: How can 8+9+10=7. Our idea is that 8,9,10 is in a number base different from the number base that the answer 7 is in. We have tried several bases but can't find the answer. Any other idea is also welcomed.

Answer 1

It could be if you take addition modulo $10$. And if we are trying to find all modulo that works we have to solve $27 \equiv _n 7$ we get $n\mid 20$ and $n>7$. So the only modulo that works are $10$ and $20$.