1. A射手射向目标，每次击中得5分，每次未击中扣3分。射手那天状态不佳，在一系列射击后，射击次数多于10次，少于20次，最终得分恰好为零。射手共射击了多少次，击中了多少次？
Solution. If the archer had $m$ hits and $n$ misses, then $5 m-3 n=0$ and $10<m+n<20$. The only pair of natural numbers that satisfy both conditions is $m=6, n=10$. Therefore, the archer shot 16 times and hit the target 6 times.