# A Holiday Puzzle: Gift Exchange

I received an email from a teacher at a school far, far away (names have been changed to protect the innocent!!). She has an interesting logic puzzle related to a gift exchange situation within her own family. This problem has really resonated with the kids. They have tried making physical representations and even attacked the problem using Microsoft Excel.

The original email is below.

Here is the situation. My husband’s family draws names for Christmas and everyone gets one other person a gift. You cannot have yourself and you cannot have your spouse. There are four couples: Bobby and Becky, Tim and Tiffany, Dave and Darla, Molly and Michael. My mother-in-law (Becky) emailed last night and told us that Bobby forgot who he has. He thought he had Dave, so she emailed me (Tiffany) and my husband, Molly and Michael to see if we had him. I (Tiffany) have Dave. So now we don’t know how to figure out who Bobby has without everyone just telling who they have. I would like to avoid this. What I know is: I have Dave and Tim has Michael. Becky has Molly. So, Bobby could have me, Tim, or Darla.

What do you think – possible or not possible?

The question is whether it is possible, given the information provided, to determine who Bobby has as his assigned gift recipient without revealing the identities of all gift recipients. Try it out and see what you can come up with!!

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