其它
The first student wrote the number $1$ on the board, the second student wrote the number $2$, and the third one and each of the following students wrote a number that was the quotient of the number written just before the last number and the last number. What did the tenth student write? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem
The ten numbers are: $1(2^{0}), 2^{1}, \frac1{2^{1}}, 2^{2}, \frac1{2^{3}}, 2^{5} \frac1{2^{8}}\cdots$  Thus the tenth exponent is $34$. 