10 people collected a total of 46 mushrooms, and it is known that no two people collected the same number of mushrooms.

How many mushrooms did each person collect?

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Let's order the people by the increasing number of collected mushrooms: $a_{0}<a_{1}<a_{2}<\ldots<a_{9}$. It is clear that $a_{0} \geq 0, a_{1} \geq$ $1, \ldots, a_{9} \geq 9$. We will leave each person with a number of mushrooms equal to their number, setting aside the excess. Then the mushroom pickers will have $0+1+\ldots+9=45$ mushrooms left. This means that exactly one mushroom was set aside. It could only have been taken from mushroom picker №9 (otherwise, two of the pickers would have had the same number of mushrooms).

## Answer

$0,1,2,3,4,5,6,7,8,10$ mushrooms.