## Logic at the 2011 Girls’ Angle Chocolate Soiree

Tonight was the 4th annual Girls’ Angle Chocolate Soiree. Many thanks to the Department of Earth and Planetary Sciences at MIT for allowing us to use their beautiful ninth floor space to host the event.

In addition to the chocolate tasting, we held a math puzzle contest adapted from one of the Treasure Hunts we held at the Girls’ Angle club. It’s become a Girls’ Angle tradition to bring in a big box of presents for the girls on the last day of every semester. But, there’s a catch! The presents are bound up in a box and locked away with combination locks. To get them, members must work together to solve math problems whose answers reveal the combinations. These hunts have proven to be a really fun, ultra-collaborative experience and the best ones have ended with the girls cracking the combinations with minutes to spare.

At our Chocolate Soiree, we modified the math puzzles from one of our Treasure Hunts and turned it into a competition…whoever could open the box first got the contents. Here’s a series of logic puzzles from the Soiree:

In each of the problems, three people, labeled A, B, and C, are having a dialogue. The labeling can change from problem to problem.  One person is positive because everything that person says is correct.  One person is negative because everything that person says is wrong.  The third person is unpredictable.  For each, identify person A as being positive, negative, or unpredictable.

Problem 1.

A: If B solved this problem, B would say I’m positive.
B: That’s right, for I did do this problem and I say A is positive!
C: Well, I solved the problem too, and I’m sure A is unpredictable.

Problem 2.

B: A and C always say different things!
C: Yeah, that’s true, it really gets annoying.
A: Well, there are times when C and I do disagree.

Problem 3.

A: Four is the maximum number of points of intersection.
C: There can be more.
B: A quadrilateral has four sides.
A: Exactly, that’s why the answer is four.
C: If the answer is four, then the answer for a triangle would be 3.
B: The answer for a triangle is 3.
C: I don’t agree with B.
B: Aren’t we talking about intersecting with a circle?
C: Yes, that’s right.
B: Oh, right, so the answer for the triangle is actually 6.
A: No, it’s 3.

Problem 4.

A: If you ask C, you’ll always get correct information.
B: If you ask A, you’ll always get correct information.

If you enjoy problems of this sort, you’ll probably enjoy books by Raymond Smullyan. He’s got a knack for making really fun, challenging logic problems.