9,10,11 |
| :---: | :---: | :---: |
|  | Division with remainder |  |
|  | Product rule |  |
|  | Cooperative algorithms  Evaluation + example |  |

Authors: Knyaz K.A., Leontyeva O.

A magician and an assistant are going to perform the following trick. A spectator writes a sequence of $N$ digits on a board. The assistant then covers two adjacent digits with a black circle. The magician then enters and his task is to guess both covered digits (and the order in which they are arranged). For what smallest $N$ can the magician and the assistant agree on a strategy to ensure the trick always succeeds?