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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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  • $\begingroup$ this is a bit harder puzzle than a simpler classic puzzle "dividing goat" $\endgroup$ – Jamal Senjaya Aug 17 '16 at 4:40
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    $\begingroup$ But similar answer, just numbers are different. $\endgroup$ – Krishnabhadra Aug 17 '16 at 4:50
  • $\begingroup$ @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. $\endgroup$ – Chris Aug 17 '16 at 14:23
  • $\begingroup$ similar to this $\endgroup$ – Angelo Aug 17 '16 at 17:44
  • $\begingroup$ 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. :) $\endgroup$ – Paul LeBeau Aug 17 '16 at 19:25
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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.

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  • $\begingroup$ This doesn't answer the question as worded. He promised half of the 102 goats, which is 51. $\endgroup$ – Ian MacDonald Aug 17 '16 at 23:02
  • $\begingroup$ @ian If you are his first son which one do you prefer 65 or 51 ? I prefer 65, So this is a win-win solution. $\endgroup$ – Jamal Senjaya Aug 17 '16 at 23:41
  • $\begingroup$ I'm sure he would prefer 102, but neither 102 nor 65 is what is written for the promise. $\endgroup$ – Ian MacDonald Aug 18 '16 at 10:58
  • $\begingroup$ Ok whoever downvoted my answer, please add reason why. $\endgroup$ – A J Aug 19 '16 at 5:13
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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.

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    $\begingroup$ 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. $\endgroup$ – Ojonugwa Ochalifu Aug 17 '16 at 12:26
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    $\begingroup$ @OjonugwaOchalifu: For all I know the uncle is good with numbers and worked it out the way I describe. $\endgroup$ – Jaap Scherphuis Aug 17 '16 at 12:40
  • $\begingroup$ Well...touché.. $\endgroup$ – Ojonugwa Ochalifu Aug 17 '16 at 12:46
  • $\begingroup$ @OjonugwaOchalifu The accepted solution is not fundamentally different from this one. $\endgroup$ – jpmc26 Aug 17 '16 at 13:55
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    $\begingroup$ 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. $\endgroup$ – GentlePurpleRain Aug 17 '16 at 20:52
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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

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    $\begingroup$ Another answer - the accepted one, in fact - has given the same answer and done so more clearly. $\endgroup$ – Engineer Toast Aug 17 '16 at 12:18
  • $\begingroup$ Welcome to Puzzling. Kindly use >! for adding spoilers in your answer. $\endgroup$ – ABcDexter Aug 17 '16 at 12:40
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    $\begingroup$ @ABcDexter: Please note that there is no consensus that spoiler markup is required in answers. It is certainly the convention, but there is nothing compelling people to do so. $\endgroup$ – GentlePurpleRain Aug 17 '16 at 23:32
  • $\begingroup$ @GentlePurpleRain I was just being nice, and tried to hint at meta :) $\endgroup$ – ABcDexter Aug 19 '16 at 12:13

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