Quiz Entry - updated: 2026.07.14
Casting out nines vs elevens — what's the takeaway for checking answers?
Each catches a different family of errors; together they're a fast, powerful sanity check, but neither proves correctness.
| Casting out 9s | Casting out 11s | |
|---|---|---|
| Uses | digit sum (mod 9) | alternating sum (mod 11) |
| Misses | transpositions, ±multiples of 9 | ±multiples of 11 |
| Catches transpositions? | No | Mostly yes |
A passing check just means "no error of that type" — it can't guarantee the answer, but a failing check is a definite red flag. Cheap insurance on any mental calculation.