1. Dima wrote a sequence of 0s and 1s in his notebook. Then he noticed that a 1 follows a 0 sixteen times, a 0 follows a 1 fifteen times, and a 0 follows 01 eight times. How many times does a 0 follow 11?
# Answer. 7.

Solution. The combination 01 appears 16 times in the tetrad, while the combination 10 appears 15 times. Therefore, the string starts with 0, meaning that before each combination 10 there is either 0 or 1. According to the condition, eight times it is 0, so the combination 110 appears $15-8=7$ times.

Criteria. Full solution - 7 points. Noted that the string starts with 0 without further progress - 2 points. Considered specific cases of concrete sequences and obtained the correct answer - 1 point. Only answer - 0.