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Problem Solving Classroom

Tips from a Master Teacher (This is a work in progress.)

Delayed Donuts

Delayed Donuts

Once a month your dad goes out on a Sunday morning and brings back a half dozen donuts for you and your sister. This month, however, he has asked you to solve a puzzle before consuming the carbohydrate explosions.

He has three donuts with chocolate frosting and three with vanilla frosting. He has labeled three bags: ch-ch, v-v, and ch-v. Then he has you turn your back while he places two chocolate donuts in one bag, two vanilla in a second bag, and one of each in a third bag. When you turn back around, he tells you that all three bags are mislabeled according to what they contain.

How many donuts must you pull out in order to determine what each bag really contains?

Difficulty: 2/5

Keywords: donuts, logic

Solution
The Solution

You only need to pull out one donut from the ch-v bag. Let's say it's a chocolate donut. Well, the other donut in the bag cannot be vanilla because that would mean the bag is labeled correctly—which it is not. So, you know that the other donut in the bag is chocolate.

One of the other two bags contains vanilla and vanilla. It can't be the v-v bag, so it must be the ch-ch bag. That leaves only the v-v bag, which must contain a chocolate and a vanilla donut.

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