2. At the New Year's celebration, schoolchildren organized an exchange game: if they were given five tangerines, they would exchange them for three crackers and a candy, and if they were given two crackers, they would exchange them for three tangerines and a candy. Father Frost played this game with them several times and received a total of 50 candies. Initially, he only had a bag of tangerines, and after all the exchanges, he had no crackers left. How many tangerines did Father Frost give to the children?
Solution. Ded Moroz conducted 50 exchanges, as he was given 50 candies. At the end of the game, he had no crackers left, meaning he exchanged all of them back. For every two exchanges of tangerines for crackers (ten given - six received), he conducted three exchanges of crackers for tangerines (six given - nine received). Therefore, every five exchanges, Ded Moroz irreversibly gave away one tangerine. All exchanges can be divided into ten such groups. Therefore, Ded Moroz gave away 10 tangerines in total.

Answer. Ded Moroz gave away 10 tangerines.