Friday puzzle -- how many cookies?

7/22/11, 2:51 AM #1

Alex Y
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Friday puzzle -- how many cookies?

Alex Y

My wife and I hosted a pot-luck cookie party. We sent invitations to about 50 people, with instructions to bring a specific number of their favorite home-made cookies.

We know that some of the people we invited were unable to come, and at least one forgot his cookies. In fact, Sam apologized to me for forgetting his cookies, but said that when he arrived, my wife said that was okay, since we already had about 20 sets of cookies from those who arrived before him, with still more likely to come.

After everyone had arrived, we put the cookies (all 1,287 of them) in a big basket, mixed them up, and distributed them equally to everyone in attendance, whether they remembered to bring their cookies or not. (There were no broken cookies; everyone got the same number of whole cookies.)

How many cookies did each person get?

Re: Friday puzzle -- how many cookies?

7/22/11, 1:46 PM #2

Larry Barrett
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Re: Friday puzzle -- how many cookies?

Larry Barrett

I see two possible anwers, both in the 30's.

Re: Friday puzzle -- how many cookies?

7/22/11, 1:54 PM #3

Alex Y
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Answer is unique

Re: Friday puzzle -- how many cookies?

7/22/11, 2:22 PM #4

Thomas Skaggs
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Re: Friday puzzle -- how many cookies?

Thomas Skaggs, Foothills of Mount Level

Why wasn't I invited?

T.

Re: Friday puzzle -- how many cookies?

7/22/11, 2:30 PM #5

Alex Y
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Re: Friday puzzle -- how many cookies?

Alex Y

You were one of the no-shows. Guess it was a problem with the invitations at the post office. Sorry about that.

Re: Friday puzzle -- how many cookies?

7/22/11, 3:11 PM #6

Larry Barrett
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Re: Answer is unique

Larry Barrett

Did 6 people show up without cookies?

Re: Friday puzzle -- how many cookies?

7/22/11, 4:19 PM #7

Alex Y
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Yes

Re: Friday puzzle -- how many cookies?

7/22/11, 7:42 PM #8

Alex Y
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Solution

Alex Y

Kudos to Larry for getting this one.

There are 1,287 cookies. Since everyone brought the same number (or 0) and everyone left with the same number, we see that we need to look at the numbers that divide evenly into 1287: 3, 9, 11, 13, 33, 39, 99, 117, ...

Since Sam brought no cookies, we know that the number bringing cookies is less than the number attending. We also know it is more than "about 20". We also know that the number attending (assuming all were invited) is less than "about 50".

The only possibility that fits these conditions is that 33 people brought 39 cookies each, and that all 39 people attending (including the six who did not bring cookies) got 33 each to take home.

Friday puzzle -- how many cookies?

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