Katie the logician

Yesterday, Katie came up with her own, consistent logic puzzle!  This is how it happened (with the puzzle, of course).

I was flipping through Alice in Puzzle-Land by Raymond Smullyan, which had just arrived in the mail.  Naturally, she asked me what I was looking at.

Me: It’s a book of stories with logic puzzles in them.  They are similar to the ones we did last year in class where there were three people and you had to figure out who was telling the truth based on what they said (and the knowledge of how many of them were lying).

K: Yeah, I remember.  When you guys acted it out, you were lying!
(I didn’t remember that part.) 🙂

K: Can you give me a problem now?

Me: I can read you one from the book.

K: No, I want you to make one up.

Me: I’m not sure I can make up a good one on the spot like that.

K: I can!

Me: Oh yeah?

I didn’t expect Katie to come up with anything interesting or consistent, but decided to let her have a go at it. I thought that maybe at least she’d learn why it’s not so easy to come up with good puzzles.  However, I was in for a surprise.  After a brief pause, Katie came up with this:

Lets pretend that we don’t know that Yulia is your sister.  In fact, she can be anyone’s sister and we don’t know whose she is.  Maybe she’s yours, maybe grandpa’s or maybe dad’s.  You say, “Yulia is my sister.”  But grandpa says, “No, Yulia is my sister.” Dad says, “Yulia is not my sister.”  But Yulia says that she is dad’s sister.  Only one person said the truth.  Whose sister is she?

It took me a moment to realize that the problem had a unique answer and to figure out what it was.  I told it to Katie, along with my reasoning, and she confirmed that it was her answer as well.  When I told her that I was proud of her for coming up with the problem and solving it, she replied, “But why?  It was easy.”  What do you think?

One final thought.  I don’t think that Katie actually thought through all the possibilties when she was coming up with the problem – there was almost certainly an element of luck involved in it all working out.  However, the most important part for me was that this made her excited about logic puzzles.  She wanted to do more right away, but it was getting very late.  We decided that we’d start reading the book with the logic puzzles the very next day.  And we did – but that’s a story for another post!

About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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1 Response to Katie the logician

  1. David says:

    I also imagine that she didn’t check first that no other answer worked. But still, wow! Did she start with what Dad and Yulia said, knowing that exactly one of them could be telling the truth, so the others must be lying?


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