A Fistful of Dollars

A boy with 10 pockets wants to distribute 44 $1 coins such that no two pockets have the same number of coins in them. Can he do it?

Notes:

All the pockets are initially empty.

The number of coins in any pocket can't be negative.

Trivia:

A Fistful of Dollars (1964) - Clint Eastwood

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