10. (10 points) 2012 students line up in a row to report numbers. If a student reports a single-digit number, the next student reports double that number; if a student reports a two-digit number, the next student reports the sum of the unit digit and 5. It is known that the first student reports 1, and by the time it reaches the 100th student, he adds another single-digit natural number to the number reported by the previous student, and no one else notices, continuing to report numbers according to the previous rules, until the last student reports the number 5. What number did the 100th student add to the number reported by the previous student? $\qquad$
【Solution】Solution: According to the rules, write down the numbers reported by the first few students: 1, $2,4,8,16,11,6,12,7$, $14,9,18,13,8,16 \cdots$ It can be observed that starting from the 5th student, every 10 students form a cycle, so the number reported by the 99th student is 7;

Since the last student reported the number 5, the second-to-last student could only report 10, and the third-to-last student could only report 5 or $15 \cdots$ Continuing this pattern, the number reported by the 100th student can only be 15, which is 8 more than the number reported by the previous student. Therefore, the answer is 8.