3.31 The marksman at the shooting range was offered the following conditions: each hit on the target is rewarded with five tokens, but for each miss, three tokens are taken away. The marksman was not very accurate. After the last ($n$-th) shot, he had no tokens left. How many shots were in the series and how many were successful, if $10<n<20$?
3.31 Let there be $m$ hits, and thus $n-m$ misses. Then $5 m-3(n-m)=0$, or $8 m=3 n$, from which $m=\frac{3 n}{8}$. Since $m$ and $n$ are natural numbers, $n$ must be a multiple of eight. In the interval $10<n<20$, only the value $n=16$ is suitable. Therefore, 16 shots were fired, of which 6 were successful.

Answer: 16 and 6 shots.