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# Did you get more than me?

## Question

Four men (A, B, C, and D) are kept in a room a punishment for their crimes.  Each day, they retreat to a corner where they are fed an amount of a certain type of food.  In total, they receive thirteen pieces of the assigned food.  On this day, they all retreated to their corners to receive beef jerky.  After enjoying their food, they came back to the center.  In front of the group, A asked B, "Did you get more than me?" To which B replied, No.  Curious then, B turned to C and said, "Did you get more than me?" To which C replied, No. Even more curious, C turned to D and said, "Did you get more than me?" To which D replied, "Yes and I know how much each of you got!"

How much food did B and C get?

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Spoiler

B and C each have 1 piece...D has X pieces (where X>1), and A has 11-X pieces.

Let's walk through this:

We are starting with the assumption that everyone got at least one piece

When A asked B if he had more and B said "no", the only way he could know that is if B only received one piece...Because with that, there is no way he could've had more than A...he could have had the SAME, but not MORE.

So then B asked C the same, and the same logic applies. So B and C each had 1 piece.

At this point we know B and C each had 1 piece, which means there are 11 pieces unaccounted for. D knows all of this information because of what he just heard, and as long as he has 2 or more, he knows he has more than C...and he would know exactly how many because A would have (11-D), which is why he can say his statement.

If our original assumption is incorrect, and people were allowed to have 0, then B and C both had 0 as CaptainEd mentioned...although D would have at least 1, not 0, and A would have the rest.

Edited by Pickett
Misread original post.
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I'm missing something.

Spoiler

[spoiler=one answer] A,B,C each got zero, D got 13[/spoiler]

Edited by bonanova
Spoilered CaptainEd's answer
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Spoiler

A, B and C got 3 pieces each, D got 4 pieces-

Edited by bonanova
Spoilered Indra's answer
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Spoiler

It is stated that D got more than C. Thus D did not necessarily get more than A or B [C<=B<=A & D>C].

Edited by rocdocmac
removed tables
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If we assume that the men are perfectly intelligent, I think this puzzle may be trickier than it seems. In fact, it appears impossible?

Like Pickett, I will adopt a positive world view and assume that each man received at least one piece of beef jerky.

Spoiler

True, B can only be sure that he got less than A if he only received one piece. Same goes for C.

However, A would only have asked if he himself had received less than six pieces. Otherwise, the answer would have already been clear to him.

So this is where it gets strange. Since C knows that B only received one piece and A less than six, he should also know that D could not have received fewer than six.

Curious.

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I think we make a wrong assumption in the assessment of A.

A asks a question and B has only 3 possible responses: "Yes," "No,"  or "I don't know."  If B has received 6 or more pieces, he would answer "Yes." If B has only gotten 1 piece, he will answer "No." If B has gotten 2 to 5 he would answer "I don't know."

A would know this before asking the question. So it does not follow that A is limited to 2 to 5 pieces. A's question is really to determine B's possible holdings.

In any case, B has to have 1, and C has to have 1.

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12 hours ago, Biotop said:

I think we make a wrong assumption in the assessment of A.

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A asks a question and B has only 3 possible responses: "Yes," "No,"  or "I don't know."  If B has received 6 or more pieces, he would answer "Yes." If B has only gotten 1 piece, he will answer "No." If B has gotten 2 to 5 he would answer "I don't know."

A would know this before asking the question. So it does not follow that A is limited to 2 to 5 pieces. A's question is really to determine B's possible holdings.

In any case, B has to have 1, and C has to have 1.

That's actually a pretty interesting point.

Spoiler

You're saying that even if A knows for sure that he got more, it's possible he is trying to determine whether B only got one piece or not (unless A got the maximum number of pieces).

Perhaps this is reading too much into the problem, but if that's the case, why wouldn't A simply ask how many pieces B got?

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On 8/8/2017 at 8:44 AM, gavinksong said:

That's actually a pretty interesting point.

Reveal hidden contents

You're saying that even if A knows for sure that he got more, it's possible he is trying to determine whether B only got one piece or not (unless A got the maximum number of pieces).

Perhaps this is reading too much into the problem, but if that's the case, why wouldn't A simply ask how many pieces B got?

Because then we wouldn't have a puzzle.

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I feel so upset. I cannot solve this problem.

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