A brain teaser

[Rankenphile]

We've had a number of interesting head-scratching threads going lately, so here's a good logic puzzle for you. It is one of my favorites, and it is absolutely solveable, if you approach it from the right viewpoint.

Scenario: You are in a completely dark room. No light can enter, so it is so dark you cannot see a thing. You have nothing with you - no flashlight, no matches, absolutely nothing. You are sitting at a chair in front of a table. On the table is a deck of ordinary playing cards. The deck has been pre-arranged for you so that exactly 13 cards are face-up, while the remaining cards are face-down. The deck has been shuffled at random. Your task is to arrange the deck into two separate piles, so that each pile has an equal number of face-up cards. The piles do not have to have the same number of total cards in them, only the same number of cards facing up. You cannot see them, but you are otherwise free to move and interact with them however you see fit. You cannot tear them or otherwise damage them. You cannot feel any difference between the faces of the cards - they are absolutely ordinary playing cards.

Question: How do you accomplish the task of creating two piles with an equal number of face-up cards?

[xmastree]

Hmm... First thing I would do, given that 13 isn't divisible by 2, is turn over one card. Depending on the state of that card you will then have either 12 or 14 face up cards.
After that I'm stuck...

Am I allowed to take them out of the room? :)

[DaveW]

Aha! Took me a while but i got it...i think.

Take both stacks and put them on their side.

I actually thought i had developed a mathematical proof but it turned out to be a part solution-it was true for every case where all 13 cards weren't in the same pile. If this sounds more like an actual solution, then let me know and i'll go over my working.

-Dave

[New Disease]

I dont think theirs anything after that Xmas. I think your right with your current answer. The number of total cards in each pile as well as the number of face down cards is irrelevant. He said you only need two piles with an equal number of cards facing up. You start with 13 face up and 39 down...

- So if you turn one card over and it was originally face up you'll have 12 cards face up and 40 cards face down.

- Alternately, If you turn one card over and it was originally face down you'll have 14 cards face up and 38 face down.

Though I must admit I scrolled down to see what the other poster got cause I was planning on tearing the deck in half to get equal parts (din't read all of the paragrah before, heh) :D

[xmastree]

There has to be something more, since turning one over still leaves you with only one pile.

[antheh]

Turn the deck on it's side and split it into two equal groups and it's done?

[Rankenphile]

No, splitting the cards into two piles on it's side isn't the answer, because neither pile would be "face up" or "face down", they would be "face left" and "face right". You guys are getting close, however.

Turning over one card in the deck and then splitting the deck into two equal piles doesn't guarantee anything, because the face-up cards are shuffled randomly throughout the deck - there is no way of knowing how many cards are now face-up and face-down in each pile.

You guys are getting warm, though. Keep going. :D

[d_stilgar]

Yeah, I'm having trouble with this one.

[Slug Toy]

ok, first of all you need to flip one card over, like everyone has said. then you have to find your way over to the wall, and turn the lights on. then finish fiddling with the cards.

[Rankenphile]

lol... not quite.

[Rankenphile]

I'll be gone for most of this weekend, although I may have time to pop in here and there on my laptop from the hotel from time to time. If nobody has the answer by Monday, I'll post the solution - but hopefully you guys can get it by then. :D

[OvRiDe]

I think it involves nightvision goggles..

[OvRiDe]

I sent a PM with my answer.. Didnt want to post it and give it away if it was right..

[Cevinzol]

I know but I'm not telling :D
(that way I can look smug and superior when the answer is posted)

[Judgement]

It took me some time to figure it out but I got a deck of cards out and went at it I wont tell the anwser but the main hint is




The piles do not have to have the same number of total cards in them, only the same number of cards facing up.

[Rankenphile]

OvRide sent me the answer in a PM, and he was correct.

And Judgement is right. That is indeed a primary clue as to the solution.

[OvRiDe]

Woohoo.. wheres my prize!!! j/k

When this one is done.. I got a pretty fun little logic problem that they asked in a job interview that I would like to share.

[Rankenphile]

Okay, here is the answer, for those of you still wondering.

In order to get an equal number of cards in both piles, you count off the first thirteen cards from the deck, then flip them over and place them next to the remaining cards.

Any cards taken from the first pile would be righted. Say you took thirteen cards and four were face up. That leaves nine face-up cards in the remaining deck. Once you flip the thirteen cards, nine will be face up and the original four would be face down. This works with any number of face-up or face-down cards.