# Knights and Liars

Last Thursday we worked on the Knights and Liars problems. E, who is generally hard to impress, was thrilled. Turns out, he loves these problems. This was the first time I’ve seen him so enthusiastic, smiling, and looking very happy.

For this first Knights and Liars round I chose problems that weren’t too difficult. For example, this one from Mathematical Circle Diaries, Year 1 by Anna Burago:

You meet a group of three islanders: Tom, George, and Betty. You ask each of them the same question: “How many knights are in your group?” Tom replies, “None.” George says, “One.” Can you find out what Betty is? What is her response?

Both E and A said they remembered some of the problems from another math enrichment program they were in last year. So to make things more interesting, I added a possibility that some of the characters could be tourists (those can either tell the truth or lie). Surprisingly, both E and A got stuck at this point. It was M, who generally stays quiet, who pointed out a couple of times that “now that we have a tourist, we need more information or we can’t solve the problem”.

We’ve done quite a few of these problems in the first part of the circle. And then switched gears and worked on a version of the Four Fours puzzle. In our version we had to use four 4s and addition, subtraction, multiplication and division to try to come up with numbers 1 through 30. E and A cranked out a few numbers. These are really A’s favorite, I think. He is very quick with calculations and tenacious when presented with tough challenges.

While E and A kept putting new equations up on the wall, M’s progress was much slower. And yet, he was the first one who realized that the fours could be concatenated into 44 and 444. This really helped A to work out an equation that got him a 2.

But herein lies the problem (for me) – to figure out how to make M’s and K’s voices heard. Fortunately, while at the National Math Festival in Washington, DC last Saturday, I got to talk about it with Rodi Steinig and she suggested a few ideas. Thank you, Rodi!