2.1 In a closed bag lie apples. Three friends tried to lift the bag and guess how many fruits were inside. The first one said that, in his opinion, there were 20 apples, the second thought there were 22, and the third said 25. When the friends opened the bag, it turned out that one of them was off by 1, another by 3, and the third by 6. How many apples were in the bag? Find all possible answers.

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# Answer: 19

Solution. Note that the first and second friends give even predictions, which means they make an error of the same parity, while the third makes an error of a different parity. Therefore, the third friend was off by 6 apples, so there were either 19 or 31 apples in the bag. Checking both options, we get the answer.