# 2.1. Condition:

In the campus, rooms are numbered consecutively $1,2,3,4 \ldots, 10,11, \ldots$ For room numbering, stickers with digits were purchased, with the digits 1, 2, and 3 being purchased in equal quantities, and the digit 5 being purchased three more than the digit 6. How many rooms are there in the campus, given that there are fewer than 100?
# Answer: 66

## Solution.

In each decade up to the sixth, the digits "5" and "6" are equal, so there are at least 50 rooms. Since the digits "1", "2", and "3" are equal, they must appear in each decade, meaning the number of rooms will be at least 53. Then the digit "5" will be four more than the digit "6". Therefore, the minimum number of rooms will reach 60, and the digit "5" will be ten more than the digit "6", as there are 11 fives among the numbers from 50 to 59 (but note one digit "6" in the number 56). Among the numbers from 60 to 66, there will be seven digits "6" and one digit "5", so the difference will decrease by 6, and the number of digits "5" will exceed the number of digits "6" by exactly four. Note that the difference in the number of digits "5" and "6" will decrease further until they are equal at number 69. If we take numbers from the next decades, the difference in the number of digits "5" and "6" will not exceed one when reaching the numbers 75, 76, or 85, 86, or 95, 96. Therefore, there is only one answer.