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- This puzzle was originally published on our Internet World
- Wide Web Site at "www.smartcode.com". If you like puzzles
- like this you might like to pay a visit.
-
- The puzzle.
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-
- Back in the 1860's, five sailors came to be marooned on a desert
- island after a violent storm at sea. They soon realised that they
- were going to need to find food, so they all agreed to go and
- collect coconuts, watched by a bewildered monkey sitting at the
- top of a palm tree.
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- At the end of an exhausting day they had a large pile of coconuts
- at the bottom of the palm tree, which they agreed to share out the
- following morning. The sailors then all went off to sleep.
-
- After a while one of the sailors woke up, and thought to himself
- "I expect there will be arguments in the morning when it comes
- time to share things out", so he decided to take his share there
- and then. He split the pile into five equal shares, and found he
- had one left over, which he threw to the monkey. He then took his
- fifth and hid it away, recombined the remainder and went back to
- sleep.
-
- Sometime later a second sailor woke up and thought the same as the
- first. He split the remaining pile into five equal parts, found
- he had one left over which he threw to the monkey, took his share
- and hid it, and recombined the now diminishing pile.
-
- Over the course of the night all the sailors did the same thing,
- and each time they split the pile there was one left over which
- was thrown to the monkey.
-
- In the morning the five sailors grouped around the now tiny pile
- of coconuts. Each knew what had happened but nobody wanted to say
- anything, so they proceeded to divide the pile into five equal
- shares, watched by a rather obese monkey! Again they found there
- was still one left over which they threw to the monkey.
-
- What is the minimum number of coconuts that the sailors could have
- collected and piled up?
-
- The solution is provided below, after a long gap of blank lines. If
- you want to try and work it out yourself may we suggest you don't
- scroll down!
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- The Solution.
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- The smallest number of coconuts possible is 15621. Try it - it does
- work!
-
- It is very difficult to calculate this directly, but there is a
- simple way of reaching that answer if you realise that for every
- answer you find, the next larger answer can be obtained by adding
- 5 to the power 6, or 15625. (6 equal divisions by 5).
-
- If you search for a small positive answer you will be out of luck,
- but how about if there is a small negative number, that while
- impossible in practice actually correctly satisfies the steps as
- outlined?
-
- If you try -4 you will find it works perfectly, as long as you throw
- the positive coconut to the monkey first!
-
- Let's take the first step. Start with -4 coconuts, throw a positive
- coconut to the monkey, which leaves you a pile of -5 coconuts. Then
- split that into 5 piles of -1 coconut each, stash one of the
- negative coconuts away somewhere, then recombine the remaining -4
- coconuts and you are back where you started, and you can continue
- the process for the six steps required (or indeed ad infinitum!).
-
- Adding 15625 to -4 will then get you to the first positive answer
- of 15621.