### BULLET BRAIN BUSTER

#### Captain Cool J

Following their latest booty gathering, the 13 pirates of the ship, Bullet Bojangles, gather at their favourite tavern to discuss how to divvy up their plunder of gold coins.

After much debate, Captain Cool J says, “Yeargggg, it must be evenly distributed amongst all of us. Yaharrgggg.” Hence, the captain begins to pass out the coins one by one as each pirate anxiously awaits his reward.

However, when Captain Cool gets close to the end of the pile, he realises there are three extra coins.

After a brief silence, one of the pirates says, “I deserve an extra coin because I loaded the ship while the rest of you slept.” Another pirate states, “Well, I should have an extra coin because I did all the cooking.” Eventually, a brawl ensues over who should get the remaining three coins.

The tavern keeper, annoyed by the chaos, kicks out a pirate who has broken a table and who is forced to return her coins. Then the tavern owner yells, “Keep the peace or all of you must go!”

The pirates return to their seats and Captain Cool J, left with only 12 total pirates, continues to distribute the coins – “one for you,” “one for you.” Now, as the pile is almost depleted, he realises that there are five extra coins. Immediately, the pirates again argue over the five extra coins. The captain, fearing that they will be kicked out, grabs the angriest pirate and ushers her out of the tavern with no compensation.

With only 11 pirates left, he resumes distribution. As the pile nears depletion, he sees that there won’t be any extra coins. The captain breathes a sigh of relief. No arguments occur and everyone goes to bed in peace.

If there were less than 1,000 coins, how many did the pirates have to divvy up?

### Answer

To find the answer, we first note that with 11 pirates the coins divided evenly; hence, the number of coins is in the list:

X=11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143…

We also know that when our answer is divided by 12 we have 5 coins left over, so we take our above list and see which of them fit, which leaves us with:

77, 209, 341, 473…

We also know that when our answer is divided by 13 evenly we are left with 3 extra coins, so if we take our list and see which numbers this works for and we are left with our answer:

341 Coins!