The Monkey and the Coconut

6. The Monkey and the Coconut

Ten people land on a deserted island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night one castaway wakes up hungry and decides to take his share early. After dividing up the coconuts he finds he is one coconut short of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey's coconut to have a total evenly divisible by 10. However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up hungry and decides to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to 1/9 of the total pile. After dividing them up into nine piles he is again one coconut short and tries to take the monkey's slightly bloodied coconut. The monkey conks the second man on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the 10th person to wake up gets the entire pile for himself. What is the smallest number of possible coconuts in the pile, not counting the monkeys?

Added 1 January 2007

Guess: Guess | Show Hint Show Solution

Hint:

Look up the formula for the LCM.

Solution:

2519

The solution for the answer is the LCM (Lowest Common Multiple) of 10,9,8,7,6,5,4,3,2,1 -1. LCM would give the least number which is divisible by all of these number and subtracting one would give us the number of coconuts which were initially there.

Comments (8)

Anonymous 17 December 2006

I think I found a mistake in 'The Monkey and the Coconut'. The lowest answer should be the product of all prime numbers below ten minus one, which is 209.

I think I found a mistake in 'The Monkey and the Coconut'. The lowest answer is not the LCM minus one, but actually the product of all prime numbers below ten minus one, which equals 209.

I found a mistake in 'The Monkey and the Coconut'. The lowest answer is not the LCM minus one, but actually the product of all prime numbers below ten minus one, which equals 209.

Anonymous 22 April 2007

I believe my answer to 'The Monkey and the Coconut' is different. I suggest that the lowest answer is the product of all prime numbers below ten minus one, which equals 209.

Anonymous 27 April 2011

The answer to the monkey and coconuts problem should be LCM +1, as there is supposed to be one extra coconut after dividing evenly.

Anonymous 16 May 2011

The least common multiple of numbers 1-10 is indeed 360. However, subtracting 1 from 360 does not yield the correct answer for the Monkey and Coconut puzzle.

Anonymous 20 October 2011

The solution of -1 also works for the monkey and the coconut problem, and it applies to any number of castaways.

Anonymous 22 November 2011

The answer given as 2519 is incorrect; we made it to 205 with the LCM and were very frustrated.

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