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I do not know the answer to this puzzle, and I found it in some old files I had

Many years ago, there was a shepherd with 3 children. One day, while talking to the owner of the herd, the shepherd was praising how smart and creative his children were. His boss decided to put that to a test and called the 3 boys to him. His words were the following:

"Here are 90 sheep. You should take them to the market next Saturday. Lewis, the oldest, will take 50 sheep; John will take 30; and Peter will take 10. The price by which Lewis negotiates his sheep should be the same for the rest of you, i.e. if Lewis decides to sell at 100€ per sheep, John and Peter should sell at the same price. You should sell all the sheep and you should earn equal amounts. I don't want any sheep back and I want to earn money from this."

The following Saturday, the brothers went to the market, sold all the sheep (Lewis sold 50, John sold 30 and Peter sold 10), the price was always the same, and each returned with equal sums of money. How?

Clarification: The price of each sheep and the amount earned by each brother should be higher than 0€. Also, selling between brothers is not considered valid.

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    $\begingroup$ Lewis gives Peter 20 sheep. $\endgroup$ – Dr Xorile May 5 at 18:54
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    $\begingroup$ @DrXorile I forgot to add something to the story that I think that forbids that, sorry. Edited. $\endgroup$ – cinico May 5 at 19:01
  • $\begingroup$ Does "selling between brothers" imply that rot13(gurl pna'g tvir zbarl gb rnpu bgure)? $\endgroup$ – EKons May 5 at 19:07
  • $\begingroup$ @EKons The original puzzle does not say it explicitly, but it seems to me that is implicit that that's not allowed. But again, I do not know the solution. I will wait a few weeks for a neat and clean solution to be answered. If not, I will accept the most original/creative one. $\endgroup$ – cinico May 5 at 19:38
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I have 2 solutions. Both are similar but use different prices.

1:

They set the price of the sheep at $600€$ per $12$ sheep and $300€$ per individual sheep.

Lewis sells $4 * 12$ sheep $= 48$ sheep at $4 * 600€ = 2400€.$ Lewis then sells his remaining $2$ sheep at $2 * 300€ = 600€.$ His total is $2400€ + 600€ = 3000€.$

John sells $2 * 12$ sheep $= 24$ sheep at $2 * 600€ = 1200€.$ John then sells his remaining $6$ sheep at $6 * 300€ = 1800€.$ His total is $1200€ + 1800€ = 3000€.$

Peter sells his $10$ sheep at $10 * 300€ = 3000€$.

2:

They set the price of the sheep at $300€$ per $7$ sheep and $900€$ per individual sheep.

Lewis sells $7 * 7$ sheep $= 49$ sheep at $7 * 300€ = 2100€.$ Lewis then sells his remaining $1$ sheep at $900€.$ His total is $2100€ + 900€ = 3000€.$

John sells $4 * 7$ sheep $= 28$ sheep at $4 * 300€ = 1200€.$ John then sells his remaining $2$ sheep at $2 * 900€ = 1800€.$ His total is $1200€ + 1800€ = 3000€.$

Peter sells $7$ sheep at $300€.$ Peter then sells his remaining $3$ sheep at $3 * 900€ = 2700€.$ His total is $300€ + 2700€ = 3000€.$

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The oldest brother paid expenses for the youngest and himself. The middle one covered only his own.

5000-4000=3000-2000=1000-0

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    $\begingroup$ Very nice answer! I don't know if this is what the OP wants, but it certainly works. $\endgroup$ – Brandon_J May 5 at 20:00
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and each returned with equal sums of money. How?

When they went to the market (and sold all the sheep for 100), Lewis went with nothing, John with 2000 and Peter with 4000 in spare change. So they all returned with equal sums of money!

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All three brothers sold all their sheep under the same price and terms and each ended up fetching the same price for them as each other. All they needed was this sign:

: :
S H E E P

5000€ for the ENTIRE FLOCK!
must buy all - will not divide flock
: :

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My answer:

When negotiating, Lewis just needs to specify that the price is divided by "the number of sheep I have". So, for example, if he negotiates the price of each sheep to "500€ divided by the number of sheep I have", then: Lewis makes 500€/50 * 50 sheep = 500€, John makes 500€/30 * 30 sheep = 500€, and Peter makes 500€/10 * 10 sheep = 500€

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Similar to @JonMarkPerry's answer, but working from the other direction:

After they made their profit (say 100 per sheep), Lewis spent 4000 at the market on some unrelated items, and John spent 2000. They all returned home with only 1000 in their pocket.

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Assuming that the brothers are benevolent to each other:

The question states they "returned with equal sums of money". It does not necessarily say that is was their own money. Perhaps Lewis' money is too heavy for him to carry himself. In that case, Peter could have offered to carry some of his brother's money, and promised to give it back after they had returned.

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