1. Dima wrote a sequence of zeros and ones in his notebook. Then he noticed that a one follows a zero 16 times, a one follows 01 seven times, and a zero follows 01 eight times. What could be the last two digits on the board? (In your answer, indicate all options and prove that there are no others).
Answer. 01.

Solution. The combination 01 occurs 16 times in the tetrad. After it, $7+8=15$ times there is a 0 or 1, and one time there is not. Therefore, one of the combinations 01 stands at the end of the line.

Criteria. Full solution - 7 points. Partial examples of sequences with the correct answer - 1. Only answer - 0 -