Twelve mothers from one school class decided to get acquainted through a bake party. They agreed that each will bring homemade cookies to share and each will try at least one cookie from everyone else. While tasting each other's cookies, each pair will have a little chat getting to know each other. How many of such little conversations were there at the party?
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4 comments:
66
Kalonni, please explain.
Otherwise, we would need a lot of baking to do to verify this :)
I just made a chart and marked an x for each pair. Then I counted the x's. I tried to post it, but it's too big... On the top row I numbered 1-12, then on the left column I numbered 1-12. For any pair that would have already met, I marked a 0. I could e-mail it to you, if you'd like. I didn't use any zany math formula for this one.
This is a good example of a puzzle where our kids may do much better than we are. My kids love doing puzzles in bed just before falling asleep. We verified your answer and it is absolutely correct: 66 conversations.
The way we did it is:
First mom has 11 conversations,
second has 10 additional conversations as she already talked to the first mom,
next one has 9 additional little chats etc.
We have:
11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
The easiest way to add this is by combining 11 and 1, 10 and 2, 9 and 3, 8 and 4, 7 and 5, and then 6.
12 x 5 + 6 = 66
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