Your Favorite Math/Logic Riddles?

shma asks: "Whether you're involved in the Sciences, Mathematics, or Engineering, you undoubtedly enjoy finding simple solutions to seemingly difficult problems. I'm sure you all have a favorite mind-bender, and who better to share it with than the Slashdot community? Post your own problems and try to solve others. Just one request: If you have figured out the solution, link to it in a post, rather than write it out where anyone can see it." What brain benders tickle your fancy? "Here's a sample to consider: You're in a dark room with 50 quarters, 18 of which are heads up. You are allowed to move around the coins or flip some or all of them, if you wish. Problem is, it's too dark to tell what you're moving or flipping (no, you can't figure it out by touch either). Your job is to split the coins into two groups, each of which has the same number of heads up coins. How do you accomplish this?"

Comments

Re:easy one

[calvin1981]

That one's really easy. Set a=42, b=0 and c=42, for any n :)

Another online version

[Enti]

http://www.websudoku.com/ is my sudoku fix of choice

Re:One possible solution:

[radtea]

Turn a light on.

I was once a judge at a "Phyics Olympics" where there was one puzzle in which students had to figure out the wiring if a circuit consisting of a couple of light bulbs and a couple of switches. They were "supposed" to solve the puzzle by flipping the switches, noting what lights were on and off, and inferring the circuit.

One team took the apparatus apart and inspected the wiring.

I gave 'em full marks.

The head judge went spare.

Science is not a game, and there aren't any rules according to which you are "supposed" to solve the problem. Alexander the Great was demonstrating the practice of experimental science when he unravelled the Gordian knot, and Feyrabend was onto something when he said, "Anything goes."

Puzzles set by humans have more to do with communication between the puzzle-setter and the puzzle-solver than anything else. Some people even decry computer-generated puzzles because of this--they say that the pleasure they get from solving puzzles comes from the feeling of interaction with another mind.