3. Calculate the sum of all natural numbers which, when divided by 27, give a quotient equal to twice the remainder.

Daniela Tilincă and Adriana Mihăilă, Brăila
## Solution:

$n=55r$ and $r<27$
$3 \mathbf{p}$
$S=55 \cdot(1+2+3+\ldots+26)$
$2 p$
$S=19305$
$2 p$