## 3. Hussar

The captain of a hussar ship divides gold coins among a trio of his hussars in the following way:

first division: one for me, one for each of you

second division: two for me, one for each of you

third division: three for me, one for each of you.

In each subsequent division, the captain takes one more gold coin than in the previous division, and gives each of the other hussars one gold coin.

How many more gold coins does the captain have in total compared to each of the other hussars after 44 divisions?

Result: $\quad 858$
## Solution.

In each distribution, the captain gives each of the three pirates one gold coin, a total of 3 gold coins.

After 44 distributions, the three pirates together have $44 \cdot 3=132$ gold coins.

The captain takes one for himself in the first distribution, two in the second, three in the third, ... and so on, up to 44 in the 44th distribution. After 44 distributions, the captain will have

$1+2+3+\ldots+44=(1+44)+(2+43)+\ldots+(22+23)=22 \cdot 45=990$ gold coins.

After 44 distributions, the captain has $990-132=858$ more gold coins than all his pirates combined.