beanz Magazine

Sailors, Coconuts, and a Monkey

Phillip Capper on Flickr

This puzzle mixes math and coding. Plus you can go online to try the code yourself.

In his book The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, Martin Gardner simplified a classic question about monkeys and coconuts. His simplified version goes as follows:

“Three sailors come upon a pile of coconuts. The first sailor takes half of them plus half a coconut. The second sailor takes half of what is left, plus half a coconut. The third sailor also takes half of what remains, plus half a coconut. Left over is exactly one coconut, which they toss to the monkey. How many coconuts were in the original pile? If you arm yourself with 20 matches, you will have ample material for a trial-and-error solution.”

To get a feel for the problem, let us guess that the sailors collect 9 coconuts.

That means the first sailor takes half of 9 (4.5) plus .5 more for a total of 5 coconuts. How many coconuts are left for the second sailor?

Well, that would be the total minus what Sailor 1 took, 9 – 5 = 4.

The second sailor takes half of the 4 (2) plus ½ more, making 2.5. That means he leaves 4 – 2.5, or 1.5 coconuts for the 3rd sailor.

Finally, Sailor 3 takes half of 1.5 (.75) plus 0.5 coconuts, for a total of 1.25.


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