Birthday Puzzle

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My class openers are getting to be my favorite part of a lot of my classes this year.  (Huge thanks to Andrew and Fawn for their part in that.  I need to do another post on how I use those two excellent resources.)  After seeing this article in the Times last night, I put the following puzzle to my students as our class opener today.

Albert and Bernard just met Cheryl.  “When’s your birthday?” Albert asked Cheryl.

Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.”  She wrote down a list of 10 dates:

May 15               May 16            May 19
June 17              June 18
July 14               July 16
August 14         August 15        August 17

“My birthday is one of these,” she said.  Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day.

“Can you figure it out now?” she asked Albert.

Albert: “I don’t know when your birthday is, but I know Bernard doesn’t know, either.”
Bernard: “I didn’t know originally, but now I do.”
Albert: “Well, now I know, too!”

When is Cheryl’s birthday?

My first instruction was for students to individually (and quietly) try to determine her birthday.  After a few minutes, I asked for a show of hands for who thought they knew the answer (sometimes one or two students, sometimes none) and told them they could then talk to neighbors, making sure to emphasize that even if they didn’t know how to figure it out, they should still discuss what they noticed and were thinking anyway – that maybe the different things they each noticed would complement each other in a productive way.  Once the discussions died down (as a result of groups either getting stuck or thinking they had an answer), I again asked for a show of hands from those who thought they knew her birthday and then told them to go find a different group to talk with.  After repeating this a few times – polling to see who thought they knew and then having the students circulate – a majority of the class had seen a good walkthrough and knew the correct answer.  At that point I let someone volunteer to explain it to the entire class and had everyone else critique the reasoning.

Every class got there (with only one needing a little guidance from me to keep from going too far down a bad track), and they were all pretty proud of themselves once they did.  One student in a later class came in saying, “I heard we’re going to do something really hard but fun today.”  Success.  We spent a bit more time on it than we normally spend on openers, but I really think it was worth it.  I’d like to do this sort of thing more often.

It’s cool how good logic starts building momentum and eventually drowns out all of the noise.  Probably most interesting for me to watch were the students who (incorrectly) thought they had the answer fairly early on.  Most would seem pretty confident about their wrong answer, but only one then refused to listen to the reasoning of her classmates and recognize her mistake (at first anyway – she came around later).  Also, I was thrilled that when one person would say, “I’ve got it,” the other students didn’t stop trying to figure it out themselves.

Does anyone regularly try stuff like this in class?  Any suggestions for how to do it better?  Anyone got a good source of similar puzzles?

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