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A father left 102 goats to his three sons. He promised 1/2 of the goats to the oldest son, 1/5 to the middle son, and 1/13 to the youngest son (maybe step son :) ). But the sons could not divide 102 evenly. Then they call their uncle, after thinking a while the uncle come with a solution, and as thanks they give the uncle 1 goat.

What is the uncle solution ?

Note : This puzzle is similiar with the sheikh dies but not duplicate since the problem has different number of animals, and the problem solver (the uncle) receive a present as thanks. (the problem solver in the sheikh dies puzzle do not receive present)

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Jamal Senjaya
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  • this is a bit harder puzzle than a simpler classic puzzle "dividing goat" – Jamal Senjaya Aug 17 '16 at 04:40
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    But similar answer, just numbers are different. – Krishnabhadra Aug 17 '16 at 04:50
  • @DylanSp: Its duplicate enough I'd have said since otherwise you run the risk of getting loads of problems like this that just differ by the numbers involved. – Chris Aug 17 '16 at 14:23
  • similar to this – Angelo Aug 17 '16 at 17:44
  • Why does the uncle need to involve his goats? And why assume he has 28? Why couldn't they could just wait until the herd has given birth to 29 kids. Then split them up as previously described (65/26/10/1). Then with the remaining 28 goats, have a feast for the village. Or sell them and split the money evenly. :) – Paul LeBeau Aug 17 '16 at 19:25

3 Answers3

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The problem with these inheritance problems is that the will is invalid.

In this case, 1/2 + 1/5 + 1/13 = (65+26+10)/130 = 101/130. So the father has not specified how to divide all his posessions, only part of them. In other words, the brothers are only entitled to about 77.7% of the fathers wealth, and the rest is in the hands of the lawyers who are needed to sort this mess out.

Now, if the sons

are allowed to divide all the goats amongst themselves, then the only fair thing is to do so in the same proportions that the father specified. 1/2 : 1/5 : 1/13 :: 65:26:10

So,

they will take the fractions 65/101, 26/101 and 10/101. As there are 102 goats, it is easiest to give one away to their favourite uncle and split the remaining 101 goats as 65, 26, 10.

The solution involving the uncle only obscures what is really going on.

Jaap Scherphuis
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    Wouldn't this answer be invalid if the riddle is solved based on the fact that the uncle came up with a solution? Your answer does not take into account the uncle's solution, on the contrary, it dismisses it. – Ojonugwa Jude Ochalifu Aug 17 '16 at 12:26
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    @OjonugwaOchalifu: For all I know the uncle is good with numbers and worked it out the way I describe. – Jaap Scherphuis Aug 17 '16 at 12:40
  • Well...touché.. – Ojonugwa Jude Ochalifu Aug 17 '16 at 12:46
  • @OjonugwaOchalifu The accepted solution is not fundamentally different from this one. – jpmc26 Aug 17 '16 at 13:55
  • I see that now. – Ojonugwa Jude Ochalifu Aug 17 '16 at 14:08
  • I agree that the will is invalid. I further state that a smarter and more fair uncle would have instead borrowed 36 goats from the herd and divided the spoils differently. This way the goat that had to be cut in half would be gifted to him for his "intelligence", and the remaining 50 goats (after returning those he borrowed) would be given to the daughters who were obviously left out of the inheritance due to the father's bigotry. – Keeta - reinstate Monica Aug 17 '16 at 14:59
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    It seems clear to me that the first son should get $\frac{102}2 = 51$ goats, the second should get $\frac{102}5 = 20.2$ goats, and the third should get $\frac{102}{13} \approx 7.85$ goats. The remaining $\approx$ 22.95 goats need to be sorted out by the will's executor. $\frac12 + \frac15 + \frac1{13} \neq 1$, so the father didn't specify where the remaining $\frac{29}{130}$ goats should go. If the brothers take 65, 26, and 10 goats respectively, they are getting $\approx$ 64%, 25%, and 10% of the goats, instead of the 50%, 20%, and $\approx$ 7.7% specified by their father. – GentlePurpleRain Aug 17 '16 at 20:52
  • I agree, adding goats to divide evenly makes no sense. The first son should get 51 goats, the second should get 21 (let's be real, no one wants $\frac{1}{5}$ of a goat, so we'll be generous and round up), and the third should get 8. The remaining 22 goats should either be slaughtered for a community feast, or perhaps the government will take them as an estate tax.

    This question should be worded in some other way that doesn't involve inheritance, where 100% of the estate should be disposed of as written (none of this "have people throw other stuff in, then figure it out" garbage)

     – Doktor J Aug 18 '16 at 14:22
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Solution:

Uncle brought his 28 goats and added in the herd, so the number of goats will be 130. Now eldest son will get 1/2 of 130 goats, i.e. 65. Middle son will get 1/5 goats, i.e. 26 goats. And the youngest son will get 1/13, i.e. 10. So the total is 65+26+10=101. Now there remains 29 goats among which 28 belong to uncle and 1 as thanks.

A J
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1 goat given as thanks hence remaining = 101.

Now this will evenly gets distributed among the sons as per father.

Let x be the total no which will get distributed therefore

$ \frac{1}{2}x + \frac{1}{5}x + \frac{1}{13}x = 101$
=> $x = 130$.

Hence,

the uncle has added 28 more goats

ABcDexter
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user28978
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