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09 Fujian college entrance examination math problems 10 and 15.
The most stupid way is to list them all, but there is a certain skill, that is, only count the number of students at a time. It is observed that a student reports 1 for the first time, 8 for the second time, 89 for the third time and 987 for the fourth time ... The rule is that the number of the nth report is equal to 1 1 multiplied by n- 1 plus the number of n-2. Until all the numbers reported by classmate A are found out. (It's better not to. It takes a lot of time, and it also tests the computing power. I secretly calculated in Chinese class and was found by the teacher ...)

A better method is to observe the fourth item in112358132134 ... and the eighth item is a multiple of 3, which proves that all 4n items are multiples of 3. A student's number is the first, sixth, eleventh ... (5n-4). Then ask only the common multiples of 4n and 5n-4 in 100.

The final answer is 5.