Good answers to this popular question came from Georgina Baxter, Suzanne Dash, Emily Savell, Helen Almand, Naomi Pearson, Catherine Renwick and Sang-mi Kim, Davison High School, Worthing; from James Dotti and Shabbir Tejani, Jack Hunt School, Peterborough; and from Rachel Walker, Christianne Eaves, Suzanne Abbott, Peggy Brett, Fiona Conroy, Nisha Doshi and Helen Battersby, The Mount School, York.
| Mod 10 | Mod 11 | Mod 13 | Mod 15 | Mod 17 | Mod 19 | Mod 21 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| 9 | 9 | 9 | 9 | 9 | 9 | 9 |
| 16 | 5 | 3 | 1 | 16 | 16 | 16 |
| 25 | 3 | 12 | 10 | 8 | 6 | 4 |
| 36 | 3 | 10 | 6 | 2 | 17 | 15 |
| 49 | 5 | 10 | 4 | 15 | 11 | 5 |
| 64 | 9 | 12 | 4 | 13 | 7 | 1 |
| 81 | 4 | 3 | 6 | 13 | 5 | 18 |
| 100 | 1 | 9 | 10 | 15 | 5 | 16 |
| 121 | m 2=0 | 4 | 1 | 2 | 7 | 16 |
| 144 | 1 | 1 | 9 | 8 | 11 | 18 |
| 169 | 4 | m 2=0 | 4 | 16 | 17 | 1 |
| 196 | 9 | 1 | 1 | 9 | 6 | 5 |
| 225 | 5 | 4 | m 2=0 | 4 | 16 | 15 |
| 256 | 3 | 9 | 1 | 1 | 9 | 6 |
| 289 | 3 | 3 | 4 | m 2=0 | 4 | 16 |
| 324 | 5 | 12 | 9 | 1 | 1 | 9 |
| 361 | 9 | 10 | 1 | 4 | m 2=0 | 4 |
| 400 | 4 | 10 | 10 | 9 | 1 | 1 |