Matěj and his friends went caroling. In addition to apples, walnuts, and gingerbread, each of the boys also received an orange. Jarda got one orange, Milan too. Radek, Patrik, Michal, and Dušan each got two oranges. Matěj got as many as four oranges, which was the most of all the boys. The other boys each got three oranges. How many boys went caroling if they received a total of 23 oranges?

(M. Volfová)
Boys whose names we know received a total of $1+1+2+2+2+2+4=14$ oranges. For the boys whose names we do not know, there are $23-14=9$ oranges left. Since each of these boys received three oranges, there must have been $9: 3=3$ of them. We know the names of seven boys, and three more boys whose names we do not know, so in total, 10 boys went caroling.

Evaluation. 2 points for determining the number of oranges received by boys with known names; 1 point for determining the number of oranges received by boys with unknown names; 2 points for determining the number of boys with unknown names; 1 point for determining the total number of boys.

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