Image: Wikimedia

This story originates from India.

A man died and left seventeen elephants to his three sons. His will said, “My eldest son gets half of my elephants, my middle son gets one-third, and my youngest son one-ninth of the seventeen elephants.”

However, there is no way you can divide seventeen elephants that way unless you cut up one of the elephants. Fortunately, though, a wise old friend had an idea. He lined up their seventeen elephants. Then he added one of his own — so they had eighteen elephants. Listen carefully!

Now it was easy — the eldest son got his half — nine elephants — the middle son got one-third of the eighteen, or six elephants — and the youngest son got one — ninth — two elephants. Add them up, you get seventeen. There was one elephant left.

The sons thanked the wise old man who said, “Now I can have my own elephant back.” And everyone was happy.

This may be both legally and mathematically incorrect but at least, no elephant was harmed!

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Alle beetjes kunnen helpen

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Hi! 🙂

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HaHA! The comments are as entertaining as the post. Wit and wisdom of elephantine proportions.

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I agree! I enjoyed reading the article and seeing the puns made me laugh!

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You may have found the true meaning of “One”.

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I always wondered whether it was possible to create a solution to a similar problem as above, but with different numbers. In other words, find X such that the sum of X+1 divided by A, B, and C would equal X. Now in the classic problem above, A=2, B=3, and C=9. Is it possible to find X given *any* A, B, and C? Anyone want to take a stab at generalizing the solution in this manner? Would there have to be restrictions placed on A, B, and C so that X would turn out to be a whole number?

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That’s an interesting question. This is similar with the Erdős–Straus conjecture which still baffles me to no end.

Using a brute-force algorithm, I found seven solutions for this Diophantine equation (1/a + 1/b + 1/c = x/x+1) (taking into account the restrictions):

7: 2,4,8

11: 2,4,6

11: 2,3,12

17: 2,3,9

19: 2,4,5

23: 2,3,8,

41: 2,3,7

It appears that these are the only solutions.

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Excellent! Now, to torture you further, suppose I am able to borrow Z elephants…is there an expression that will express possible solutions for X in terms of A, B, C, and Z?

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That would certainly torture my computer and I don’t know if it can handle it.

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Fair enough; the results of your investigation then lead me to propose a new related problem with a cool solution:

“Hey Mary,” said John. Yesterday I read about a cool problem on a blog called Fun Facts. It was about a man who died and gave fractions of his elephants to his three sons. A neighbor solved the problem by lending an elephant, and then taking it back at the end.”

“Oh really?” said Mary. “How many elephants did he start with?”

“I don’t know. I forgot.”

“Well then, what fractions did the sons get?”

“I don’t know. My memory is terrible; can’t remember that either.”

“You’re hopeless, John.”

“All I remember is that the next day the neighbor realized he had misread the will, and the fractions for each son were wrong. But he corrected himself, lent an elephant again, and it all worked out like before.”

“”Oh,” said Mary. “Why didn’t you say that before? Now I know how many elephants the man had.”

How many elephants, and how did Mary know?

Of course, the solution to that is obvious once we look back at your list. But I think it’s a very good puzzle for those who have never seen your list.

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Having 3 sons myself this seems a good ruse to keep them happy – apart from my lack of elephants. They all seem to get just over the 1/2, 1/3 and 1/9th. The fact that those fractions only add up to 17/18 ie less than 1 (the whole) doesn’t seem to bother them!

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Love it!!

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You guys are stealing my punder (and I thought my puns were above re-poach — what a letdown).

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That’s mathematically irrelephant!ﾍ(=￣∇￣)ﾉ

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I herd that ivoryone refused to talk about the elephant in the room so they all agreed with the compromise even if it’s mathematically and legally irrelephant. Hmm, perhaps, the old man who suggested the solution was seeing pink elephants…

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Seeing pink elephants? Ahh, yes, you mean they’re trunk. Anyway, I guess this is a thankless tusk. ∩(︶▽︶)∩

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The tusk wasn’t that mammoth of a deal so it’s ok I suppose.

Though the old man’s opinion carried a lot of weight huh?

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Hahaha…thanks a ton! You’re the master of puns!（*’∀’人）

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In Alabama, the Tuscaloosa.

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kudos

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