Comments on: FW. Walk Around the Clock

By: Shawn

Shawn — Tue, 05 Jun 2012 21:12:29 +0000

Well, it seems that if the probability of the coin coming up heads is 0 or 1, the only movement will be clockwise or counterclockwise respectively, so it will always be 4 3 2 1 12 or 4 5 6 7 8 9 10 11 12. Whatever function models this probability should yield an output of 0 if the input is 0 or 1.

By: strauss

strauss — Wed, 18 Apr 2012 14:53:29 +0000

Gosh it's been a long time since I've thought about this puzzle; but I'm pretty certain that the answer isn't pi/4! A quick experimental run gives success about 9% of the time, with a fair coin.

(Note too the problem asks for the general solution, too, with a possibly weighted coin)

Let me try to recall how the heck this problem works. The vague idea, which the next post is a clue, is to express the likelihood of success from a given position in terms of the success from neighboring positions-- it turns out it's a special weighted average. But missing all the details... (There is some cleverness needed to set it up right in the first place)

By: Shawn

Shawn — Tue, 10 Apr 2012 05:39:42 +0000

The probability has gotta be pi/4.

By: strauss

strauss — Mon, 06 Jul 2009 21:24:54 +0000

I don’t quite see how that would be helpful– what’s your idea? I can see one way to use an 11×11 matrix, but there’s a simpler approach (which, as one might guess, uses the next post!)

By: Steven H. Noble

Steven H. Noble — Fri, 03 Jul 2009 01:49:28 +0000

I’m guessing if I’m trying to find the null space of an 11×11 matrix to solve this problem I’m missing out on a more straight forward solution?