Problem 8-4. In the garden of the oracle, there live four turtles. A visitor can choose any subset of turtles in a move and ask the oracle how many of these turtles are males (the oracle's answers are always truthful). What is the minimum number of moves required to find out the gender of all the turtles?

Answer: 3.
Solution. In three questions, the answer can be obtained as follows. The first two questions are about turtles 1 and 2, and 2 and 3. If at least one of the answers is 0 or 2, we know who they are for the corresponding pair, and for the remaining one of the three, we know from the other question, leaving one question for the 4th turtle. If both answers are 1, then turtles 1 and 3 are of the same gender. Then we ask about $1, 3, 4$. We will hear an answer of at least 2 if turtles 1 and 3 were males, and an answer of no more than 1 otherwise. In this case, the gender of turtle 4 is also uniquely determined, and one question remains to determine the gender of turtle 2.

We will prove that two questions are insufficient. First, note that: a) in one question, without knowing the total number of males, we cannot figure out even two turtles; b) knowing the total number of males, we can figure out two, but not three turtles. Therefore, in the situation with four turtles and two questions, asking the first question about all turtles at once or about one turtle is meaningless. Since when asking about a group of three or two turtles, we can hear an answer of 1, such a question will also not lead to success.

| Rating | Score | Content of the criterion |
| :---: | :---: | :--- |
| + | 20 | Complete solution |
| $+/-$ | 14 | Correct answer, but not proven that it cannot be less |
| $+/ 2$ | 10 | Correct answer with minor flaws in the solution and not proven that it cannot be less |
| .- | 4 | Attempt to analyze cases with 2 and 3 questions, but made an incorrect conclusion that the minimum number is 4 |
| - | 0 | Solution is completely incorrect/only answer |