1. In Fedia the gardener's garden, there is a wonder-tree with seven branches. On each branch, either 6 apples, 5 pears, or 3 oranges can grow. Fedia noticed that there are fruits of all types on the tree, and the most pears have grown, while the fewest apples have grown.

How many fruits have grown on the wonder-tree?

$[3$ points $]$
Space for answers

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# Problem 1.

Answer: 30.

Since the tree ended up with fruits of all kinds, there must be at least one branch with apples, meaning there are no fewer than 6 apples. Since apples are the fewest, oranges must have grown on at least three branches, meaning there are at least 9.

There are three branches left. Suppose that on one of them, pears did not grow. Then pears grew on no more than two branches, which means there are no more than 10 pears. In this case, on another branch, either apples grew, which would make 12 apples, or oranges, which would also make 12 oranges. In both cases, pears would not be the most, so our assumption is impossible. Therefore, on one branch, 6 apples grew, on three other branches, 3 oranges each, and on the remaining three branches, 5 pears each. In total, $6+9+15=30$ fruits.