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An old farmer passes away in his sleep. After a suitable period of mourning, his three sons find their father's will in his study.

Amongst other, simpler bequests is the following:

"I wish my small flock of sheep to be well cared for, with the responsibility split between my three suns. Therefore take the pack of cards from my desk drawer, pull out three aces which you will place face up on the desk, then deal out the first three cards from the pack below them to form three fractions. These are the portions into which i wish my flock to be split between my sons."

The sons do as requested, pull out the aces and deal out the three cards, which are a 2, a 3 and a 9, forming fractions one-half, one-third and one-ninth.

Then they go out into the field and count the flock, which turns out to contain 17 sheep.

What cunning sheep-accountancy trick can they use to split the flock according to their father's instructions, without amputating any ovine limbs?

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  • $\begingroup$ Yep, it does look the same. Not sure where the cards came from in the version I heard. $\endgroup$
    – IanF1
    Commented Oct 17, 2014 at 22:42

3 Answers 3

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I think there was a similar puzzle somewhere here.

Borrow one sheep from somewhere else so you have 18. Split in 1/2 (9), 1/3 (6), 1/9 (2).

9+6+2 = 17

Now give back the borrowed sheep.

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  • $\begingroup$ That's exactly what i was after. Sorry if it's already been asked, i couldn't find it. $\endgroup$
    – IanF1
    Commented Oct 17, 2014 at 21:28
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I'd go with 9, 6, 2 for the sheep, which works out fairly well.

Between the first and 2nd son, the ratio is 3:2, which the same as 1/2:1/3. Likewise between the 2nd and 3rd (6:2 = 1/3:1/9). And the same for 1 to 3 (9:2 = 1/2:1/9).

Or, you could say that the total share of the sons adds up to 17/18. So, each son gets his share times 18/17.

So, 1/2 * 17 * 18/17 = 9.

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  • $\begingroup$ Very close to the answer I was after - but there's a trick! I'll edit the question to include something to that effect. $\endgroup$
    – IanF1
    Commented Oct 17, 2014 at 21:07
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They borrow a sheep from another farmer! Then split up in the ratios: 1/9 = 2 sheep 1/3 = 6 sheep 1/2 = 9 sheep That's 17 sheep altogether and then they can return the borrowed sheep!

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  • $\begingroup$ Oh, I was too slow! Lol... $\endgroup$
    – Ali
    Commented Oct 17, 2014 at 21:30
  • $\begingroup$ Well done but unfortunately user1071777 got there first! But +1 from me anyway $\endgroup$
    – IanF1
    Commented Oct 17, 2014 at 21:31

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