# Four people Andy, Bob, Chris and Don who ate 11 apples. Each ate at least 1 apple, and all of them know this...

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There were 11 apples.

There are four people, Andy, Bob, Chris, and Don who ate the 11 apples.

Andy, Bob, Chris, and Don each ate at least 1 apple, and all of them know this.

Andy says, “Bob, did you eat more than I did?”
Bob replies, “I don’t know. Chris, did you eat more than I did?”
Chris replies, “I don’t know”

After hearing this conversation, Don was able to figure out exactly how many each person ate.

How many apples did each person eat?

posted May 25, 2018

+1 vote

If any one has eaten 4 apples, he has eaten most of apples.
Let's analyze things:
Andy- asks, “Bob, did you eat more than I did?” - Andy certainly hasn't ate more than 4 apples, so
Bob replies, “I don’t know. Chris, did you eat more than I did?” - Bob hasn't ate more than 4 apples too, but he also hasn't eaten only 1 apple either because he would've known that he hasn't ate more than Alexandra. So,
Chris replies, “I don’t know.” - Chris hasn't ate more than 4 apples too, but he also hasn't eaten exactly 1 or 2 apples either because he would've known that he hasn't ate more than Bob. So,
Then Don figures out the numbers- The only way Don could've found this is if he'd eaten a number of apples which implies unique combination of others' apples ie. if there had been unique. The only unique combination is a minimal sum - 1+2+3+5=11
Any- 1
Bob- 2
Chris- 3
Don- 5

Let:
Andy = A
Bob = B
Chris = C
Don = D

Andy: Did you eat more than I did, Bob?
A < 4
A < B

Bob: I don’t know. Chris, did you eat more than I did?
B < 4
B ≠ 1
B < C

Chris: I don't know.
C < 4
C ≠ 1 or 2 because otherwise C < B

The only way that Don could have found is if he'd eaten a number of apples, which implies unique combination of others' apples.
i.e. If all four boys' apples had been unique, the only unique combination is the minimum sum.
e.g. A + B + C + D = 11

A = 1
B = 2
C = 3
D = 5

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