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View Full Version : OT - What we need around here is a good online puzzle...

QuikSand
02-05-2004, 08:42 AM
We've had, from time to time, some fun working together (or competitively) on various puzzles and games online. I'm itchy for more of the same.

Anyone have any links to puzzles, games, or the like that might make for some good fodder for the crowd here?
cuervo72
02-05-2004, 08:46 AM
We've had, from time to time, some fun working together (or competitively) on various puzzles and games online. I'm itchy for more of the same.

Anyone have any links to puzzles, games, or the like that might make for some good fodder for the crowd here?

hxxp://www.flooble.com/perplexus/
QuikSand
02-05-2004, 08:49 AM
Okay, the most recent unsolved puzzle from the flooble site is right here:

Two identical pack of cards A and B are shuffled throughly. One card is picked from A and shuffled with B. The top card from pack A is turned up.
If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?
Airhog
02-05-2004, 09:08 AM
1 in 52?

Probably not the right anwser, because that would be far to easy.

A coin could flip 100 times and land on heads but that doesnt mean the next flip is anything but 50-50
Nyarlahotep
02-05-2004, 09:10 AM
I think you forgot about the card that got moved over.
QuikSand
02-05-2004, 09:10 AM
Airhog, I think you're a letter off.
Huckleberry
02-05-2004, 09:11 AM
.0192378838327784
QuikSand
02-05-2004, 09:17 AM
Well, here's my solution.

We have two layers to this -- there's the case where the Kh was moved from deck A to deck B, and the case where some other card was. At first, this seems like a 1/52 vs 51/52 probability - but I don't think so. Since we know that the Qh was not moved, there are only 51 cards that could have been moved from A to B. So, I believe the chance that the card moved was the Kh is actually 1/51.

Then, we have to multiply each case by the associated conditional probability that the top card in deck A is Kh. That should be easy.

So, the model is this:

P(Kh moved) x P(Kh on top) = 1/51 * 2/53
plus
P(Kh didnt move) x P(Kh on top) = 50/51 * 1/53
equals
(2 + 50) / (51 x 53) = 52 / (51 x 53) = 52/2703.


edit: ugh. 50 * 1 = 50, not 51.
Airhog
02-05-2004, 09:20 AM
okay once again I show how much of a dumbass i really am :D
Huckleberry
02-05-2004, 09:31 AM
I got lazy. I just said 1/53 + (1/51)/53.
Franklinnoble
02-05-2004, 11:45 AM
2/3