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There are two people eating bread. One of them has 5 loaves of bread; the other one has 3. They invited a third person to eat with them. They ate all 8 loaves of bread, and out of appreciation he gave them 8 cents.

How should they divide the money to be fair?

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  • $\begingroup$ Who gave away the 8 cents? $\endgroup$
    – hat
    Commented Dec 24, 2018 at 16:16
  • $\begingroup$ @hat The third person I would think $\endgroup$
    – deep thought
    Commented Dec 24, 2018 at 16:18
  • $\begingroup$ @hat the third person gave them money for thanks $\endgroup$
    – Dear
    Commented Dec 24, 2018 at 16:58
  • $\begingroup$ Can you verify each man ate the same amount of bread? $\endgroup$
    – Longspeak
    Commented Dec 24, 2018 at 20:51
  • 1
    $\begingroup$ Does this answer your question? Five loaves and the extra traveller $\endgroup$
    – Hemant Agarwal
    Commented Jul 14, 2023 at 22:12

2 Answers 2

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They should

not divide it 5:3, as you might think, but rather 7:1.

The reason being

Although the first person provided 5 loaves and the second person 3, they each also ate some of their own loaves. If we assume they each ate an equal amount, then they each ate 8/3. So, the first person really provided 5 - 8/3 = 7/3, and the second person provided just 3 - 8/3 = 1/3. So, out of the 8 cents the third person gave, the first person should get 7 cents, and the second person 1.

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  • $\begingroup$ Before the third person was going to join, one person was going to eat 5 loaves and the other 3 loaves. Why would the introduction of a third person mean they're going to eat the same amount? I'd expect the 5-loaf person to give 5/3 loaves, and the 3-loaf person 3/3 loaves. The ratio of bread given is then 5:3, as is the correct division of the money. $\endgroup$
    – MooseBoys
    Commented Dec 24, 2018 at 21:26
  • $\begingroup$ @MooseBoys - On the other hand, maybe they were planning on eating four each. And if not, who says they gave 8/3 to the third guy. And where do they find three cent loaves of bread anyway! Perhaps there is a creative and funny alternative way to answer this question :-) $\endgroup$
    – deep thought
    Commented Dec 24, 2018 at 21:38
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really the answer is simple, given that the question is how should they divide the money to be fair? referring to the first 2 people, to which the first one contributed 5 loaves and the second 3 = 8 loaves and they decided to INVITE a third person which in gratitude gave them 8 cents. based on the only information that at the beginning were two people who together had 8 loaves and invited a third person and NEVER specified how much each one ate, but nevertheless if they specify that among the 3 they ate all 8 loaves and there is a gratification of 8 cents for the first 2 people. so each of the first person gets 1 cent for each bread contributed, the first person contributed 5 loaves of bread and 5 cents, the second person contributed 3 loaves of bread and 3 cents

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