Problem 2. There are 22 batteries, 15 of which are charged and 7 are discharged. The camera works with three charged batteries. You can insert any three batteries into it and check if it works. How can you guarantee to turn on the camera in 10 such attempts?
Solution. Let's number the batteries: $1,2, \ldots, 22$. The first six tests will involve inserting batteries into the camera as follows: $1,2,3 ; 4,5,6 ; \ldots, 16,17,18$. If at least one of these groups turns on the camera, everything is fine. If not, then among the first 18 batteries, there are at least 6 discharged ones, which means that among the last four batteries, there is at most one discharged one. The next four tests will involve trying all combinations of the remaining batteries: $19,20,21 ; 19,20,22 ; 19,21,22 ; 20,21,22$ - and we will definitely find a group of three charged batteries.

- See also problem 1 for 10th grade.
- For an answer without justification - 0 points.