A problem by Nathan Blanco

Level pending

A ship was hit by a terrible storm. The ship would have sunk if not for the help of 3 sailors. To reward them, the captain gave the 3 sailors a chest full of coins to open at the next dock. After, they all went to sleep. During the night, one of the sailors awoke, divided the coins into 3 piles, and decided to take his share of coins. However, after dividing the coins, he found one left over. Quietly, he tossed the extra coin into the sea and went back to sleep. The second sailor did the same soon after, unaware of the first sailor's actions. He too divided the coins, took his share, found an extra coin, tossed it into the sea, and slipped back into bed. Later, the third sailor did the same, and also found an extra coin, which was tossed into the sea. In the morning at the docks, a tax-collector helped divide the coins and found one extra coin which he took. How many coins were there at the start?


The answer is 241.

Nathan Blanco by Nathan Blanco , 21, USA

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1 solution

Unstable Chickoy
Jun 3, 2014

Let y y be the number of coins in each pile and x x be the total number of coins.

2 [ 2 ( 2 x − 2 3 ) − 2 3 ] − 2 3 − 1 = 3 y \frac{2[\frac{2(\frac{2x-2}{3})-2}{3}]-2}{3} - 1 = 3y

I got whole number values of

x = 79 x = 79

x = 160 x = 160

x = 241 x = 241

by checking, seems that x = 241 x = \boxed{241} would fit for the solution.

I think this problem could be solved by m o d 3 \mod{3} (I'm not sure). I don't have the knowledge on how to operate the same. :D

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