Printable

2013 AMC 10A Problem 21

Include the solution Back to the problem

2013 AMC 10A Problem 21AMC 10 Step by Step

Name: Date: September 13, 2026

Divisibility & Factors · difficulty 4 of 5 · about 7 min · position P21-25

A group of $12$ pirates agree to divide a treasure chest of gold coins among themselves as follows. The $k^{\text{th}}$ pirate to take a share takes $\frac{k}{12}$ of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins. How many coins does the $12^{\text{th}}$ pirate receive?

A)
$720$
B)
$1296$
C)
$1728$
D)
$1925$
E)
$3850$

2013 AMC 10A Problem 21

Working