## Puzzle #175: The Three Bag Puzzle

Apologies for a long break, I was in the middle of some hectic travel, both for personal and business reasons. But normal service resumes 🙂

Thanks to Suman Saraf yet again for recommending this puzzle. A variation of this puzzle was posted very early when I started 4 years back. Here it goes:

There are three children. These children need rewarding for good behaviour. I have six gifts.

• I have three chocolate bars.

• I have three giant lollypops.

Each child is going to receive two presents and, so they don’t know who is getting what, I put each pair of presents inside a brown paper bag and seal them. Only I know the distribution of the treats, but all the children know there are three of each treat and two treats in each bag.

The first child collects her bag and looks inside to see what presents she received. A curious neutral third party asks this first child a question to determine the breakdown of presents in her bag. The catch is that the child can only respond with the answers: “Yes”, “No” (or “I don’t know”). The child is a perfect logician, and always answers truthfully. What question can the outsider ask to determine the contents of the first gift bag?

What question can you ask the first child to determine the breakdown of presents in her bag?

For the purposes of this exercise, we can assume the chocolate bar and the lollypop have the same mass; This is meant to be a purely logic puzzle and does not rely on physical differences between the bags. There is no trick, gotcha, or tomfoolery in the answer.

Remember, the child can only answer your question with, “Yes”, “No”, or “I don’t know”.

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

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### 2 Responses to Puzzle #175: The Three Bag Puzzle

1. Three cases are possible:

Case 1: First bag has CL. Then the other ywo bags could be (CC, LL) or (CL, CL)
Case 2: First bag has CC. Then the other ywo bags will be (LL, CL)
Case 3: First bag has LL. Then the other two bags will be (CC, CL)

Question is: Would one of the other two guys get CC?

2. Vishal Poddar says:

He asks if any of the other two have 2 chocolate bars?

If yes, then she has 2 giant lollypops.
If no, then she has 2 chocolate bars.
If I dont know, the she has one of each.