A mathematical who-done-it?

Sue tells me her oldest has discovered the joy of logic problems. Here's a fun one from the exercises in Enderton's A Mathematical Introduction to Logic:

There are three suspects for a murder: Adams, Brown, and Clark. Adams says "I didn't do it. The victim was an old acquaintance of Brown's. But Clark hated him." Brown states "I didn't do it. I didn't even know the guy. Besides I was out of town all that week." Clark says "I didn't do it. I saw both Adams and Brown downtown with the victim that day; one of them must have done it." Assume that the two innocent men are telling the truth, but that the guilty man might not be. Who did it?

pic by martinmaters

The Improbable Power of Exponentiation

If you are a math teacher, you're probably familiar with this activity.

Get a big sheet of paper and a good paper cutter. Cut the sheet in half, and stack the pieces together. Turn the pile 90 degrees, cut it in half again, and stack the cut pieces again. Keep doing this until you've cut and stacked the sheet 100 times.

If your cutter is really good, so that it cuts a thick stack of paper as quickly and easily as a single sheet, and it takes ten seconds to make a cut, stack the pieces, and position them for the next cut, then you'll be finished in 16 minutes, 40 seconds.

If the paper is 0.1 millimeter thick (about 0.004 inch), like ordinary medium-weight letter paper, then a stack of 500 pieces would be 50 millimeters (about 2 inches) thick.

The question is: How thick will the pile be after you cut and stack the paper 100 times?

Jay sent in a nice website to guide students through the activity. Make sure to look at the answer. Jeff Root does an excellent job at getting one to understand in a physical way 2^100.

Feather Knot

I ran into this Kate MccGwire sculpture via Drawn!. Kind of reminds me of a knot problem. I'm also thinking, how long did it take to place all of those feathers? I thought Algebra was for the patient.

I play Spaghetti and Math Balls

Sue brought this in for her Number Systems class. Her youngest, Nick, is a budding math geek and this is his game. Here's how you play. One moves along the board by answering basic addition and subtraction questions. Each time you pass start you get a meatball. The goal is to be the first one to fill your bowl with six meatballs. Warning: this game can make you hungry. Bon Appetit!

pics from BoardGameGeek

The Worst Reason to Study Math

All over China, parents tell their children to stop complaining and to finish their quadratic equations and trigonometric functions because there are sixty-five million American kids going to bed with no math at all.
- Michael Cunningham

A friend forwarded this to me recently. I get sent a lot of quotes and stats of this flavor. I appreciate the aid in trying motivate my students to do math. I'm always looking for another tool in the, "When will I ever use this" battle. However, something about these quotes always seems to turn my stomach. It is either the tatic of fear-mongering or the unanalyzed assumption that the world is ultimately a better place if America continues it's preeminence among nations. I'm wondering what your reactions are? I'm looking forward to some good comments.

May Issue of Wired

I really enjoyed the new issue of Wired. It's put together by guest editor, J.J. Abrams, who I'm ashamed to say I've never heard of, but whose issue as an homage to puzzling. He comes at it from various angles from a feature story of an artist who has been able to stump the best cryptographic minds in the world to an "enigmatrix" of the network connections between math, board games, plot, mysteries, magic code, and game theory. Best of all, it is full of puzzles. Enjoy the one above!

Geek Goodness

Mike Z sent me a really a great link that will allow you to use your geek powers to feed the world. The site is called FreeRice. When you enter FreeRice, you get a math question like 13 * 5. If you answer the question correct, you have just donated 5 grains of rice to the UN World Food Program. You can play as long as you want, so fill up your bowl. If you get tired of math questions, you can always switch to something else like vocabulary words or chemical symbols. Who pays for all that rice? I just filled up a bowl and my sponsors were World Hunger Relief 2008, Unilever, and a private donor. Pretty cool, huh. Thanks, Mike!