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Author Topic: The Monkey and the Cocounts  (Read 1493 times)
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patrickosmith

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« on: May 05, 2015, 07:07AM »

A short story by Ben Ames Williams, entitled "Coconuts," appeared in the October 9, 1926 issue of The Saturday Evening Post. The story concerned a contractor who wanted to prevent his competitor from winning an important contract. A shrewd employee of the contractor, who knew of the competitor's passion for recreational mathematics, presented him with a puzzle so exasperating that while he was preoccupied with solving it he was not able to enter his bid before the deadline.

Here is the problem exactly as the employee in the William's story phrased it:

"Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food, piled them all up together and then went to sleep for the night.

But when they were all asleep one man woke up, and he thought there might be a row about dividing the coconuts in the morning, so he decided to take his share. So he divided the coconuts into five piles. He had one coconut left over, and he gave it to the monkey, and he hid his pile and put the rest all back together.

By and by the next man woke up and did the same thing. And he had one left over, and he gave it to the monkey. And all five of the men did the same thing, one after the other; each one taking a fifth of the coconuts in the pile when he woke up, and each one having one left over for the monkey. And in the morning they divided what coconuts were left, and they came out in five equal shares. Of course each one must have known there were coconuts missing; but each one was as guilty as the others, so they didn't say anything. How many coconuts were there in the beginning?"

Variation of the problem:
Rather than dividing equally in the morning, if there is again one coconut left over (which they give to the monkey), then how many coconuts were there in the beginning?

HINT:
There are an infinite number of solutions which differ by a multiple of the same composite integer.
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patrickosmith

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« Reply #1 on: May 11, 2015, 07:14AM »

Here's one explanation that gives you an answer.

https://www.youtube.com/watch?v=U9qU20VmvaU


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robcat2075

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« Reply #2 on: May 11, 2015, 08:20AM »

I kept waiting for some sort of clever punchline involving the monkey.
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Robert Holmén

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robcat2075

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« Reply #3 on: May 11, 2015, 09:56PM »

Well, i didn't understand the math in the video but by simulating the transactions on a spreadsheet i convinced myself that 3121 is indeed a solution.
 
-4 also works if we can presume the existence of anti-coconuts.


I actually like -4 better because, seriously... five guys wash up on a beach after a shipwreck and the first thing they do is collect 3000+ coconuts?

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Robert Holmén

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tbn ervin

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« Reply #4 on: Jul 20, 2015, 02:06PM »

I tried to solve it by myself for a while and didn't get too far (I must admit that I assumed that we need quite a lot of coconuts for such a calculation to take place with integers).
Than I watched the video, and realized that my math skills are quite behind for this kind of question BUT, that's a very nice puzzle with a nice story. The fact that they collect coconuts somehow stresses the fact that the solution MUST be integers (coconuts are strong and are not split easily...).
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