Riddles

[gfish]

Friday night, after the SRVC results were announced, most of us went out drinking. We ended up at a pretentious little place that sold crazy Belgian beers. It was rather more expensive than I'm used to, but worth it. Each bottle was a meal's worth of flavor and substance. And as we sat there getting rather drunk, we fell into a (logic) riddle contest. It was a lot of fun, and not just because I had a lot of luck figuring them out.

One of them completely stumped me, so I spent a good amount of the flight home working on it. I didn't solve it until I had generalized it into a set of equations, but I can see how one could figure it out directly. Since I had some much fun working on it, I thought I'd share.

You're given n coins under a towel and told that m of them are heads up. (The numbers don't matter, beyond the obvious restriction that 0 < m < n.) You can stick your hands under the towel to manipulate them, but you can't in any way sense which ones are heads up. How do you separate them into two piles (possibly of different sizes) such that each pile has the same number of heads? We're looking for a real solution, not something "clever" like 'stand them all on their edges'.

I'll post the solution in the comments.

Comments

[carmiel.livejournal.com]

If not able to feel the pattern on the coins, which I can normally do, I'd most likely count the coins and sort them into even piles stacked in two columns. Since there is only a 50-50 chance of heads regardless of what came before, the result should be very close to perfect.

NOW, I'll read the solution and see how close I got. :D

[carmiel.livejournal.com]

not as close as I would like. I forgot to flip them. :(