173. In the Olympiad, 55 schoolchildren participated. All of them submitted their work. During the checking of each problem, one of three grades was given: «+» - the problem was solved, «-» - the problem was attempted, «0» - the problem was not attempted. After checking all the works, it turned out that in no two works did the number of «+» grades and the number of «-» grades coincide simultaneously. What is the smallest number of problems that could have been offered at the Olympiad?
Instruction. If the number of tasks was $a$, then

$$
\frac{(a+1)(a+2)}{2}=55 \text { when } a=9 .
$$

A n s w e r: 9 tasks.