Question

Three sailors weremarooned on a deserted island that was also inhabited by a band ofmonkeys. The sailors worked all day to collect coconuts but weretoo tired that night to count them. They agreed to divide them upequally the next morning.

During the night, one sailor woke up and decided to get his share.He found that he could make three equal piles, with one coconutleft over, which he threw to the monkeys. Thereupon, he had his ownshare and left the remainder in a single pile.
Later that night, the second sailor awoke, and, likewise, decidedto get his share of coconuts. He also was able to make three piles,with one coconut left, which he threw to the monkeys.
Somewhat later, the third sailor awoke and did exactly the samething with the remaining coconuts.
In the morning, all three sailors noticed that the pile wasconsiderably smaller, but each thought that he knew why and saidnothing. When they then divided the remaining coconuts equally,each sailor received seven and one was left over, which they threwto the monkeys.
How manycoconuts were in the originalpile?

Answer 1

x = 690

Explanation:

Let´s call x the number of coconuts at night ( at the original pile )

Then the first sailor took x/3 threw 1 to monkeys, therefore, number 1 sailor used x/3 + 1 and left

x - ( x/3 - 1 ) = (3x - x - 3 )/3 = ( 2x - 3 )/3

Evaluating the second sailor

He took [ ( 2x - 3 )/3]/3 ] threw 1 to monkeys

[ ( 2x - 3 )/3]/3 ] + 1 = ( 2x + 24 ) / 9

The third took

[( 2x + 24 ) / 9] /3 and threw 1 to monkeys

{ [( 2x + 24 ) / 9] /3 } + 1 = (2x + 51 )/27

Finally they divided the pile each one of them got 7 and threw 1 to monkeys

The resulting equation is:

( 2x - 3 )/3 + ( 2x + 24 ) / 9 + (2x + 51 )/27 + 21 + 1 = x

Solving for x

18x - 27 + 6x + 72 + 2x + 51 + 594 = 27x

-x = - 690

x = 690