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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?"
Simply place any 18 coins into the second group and flip those over.
If you flip a coin over that was heads, it is now tails and is eliminated from consideration. If you flip a coin over that was tails, it marks with heads a coin selected that was not heads. Therefore after 18 coins are flipped, the number of heads in the second pile is equal to the number of heads that are left in the first pile.
I know lots of people have commented on using the hot/cold method to determine which bulb is which, there's another problem with that as well: You don't know the initial state of the bulbs.
Say for example all the bulbs are initially ON, and you flip two of the switches to what you think is on. Then when you flip one of them to what you think is "off" and wait a while, and go in to the room, you'll find two bulbs on, but you'll misidentify them because the one you thought you switched to "off" you actually turned "on". Not to mention they could be in mixed states initially..