card puzzle

[albionmoonlight]

Here is a puzzle that recently was featured as the Car Talk Puzzler.

You are in a completely dark room (i.e. you can't see). I give you a deck of cards and tell you that 10 cards in that deck are face up, and the rest are face down. The face-up cards are in the deck completely at random.

I then ask you to take the deck and make it into two stacks of cards that contain the same amount of face up cards.

How do you do it?

[QuikSand]

Got it. Clever puzzle.

[Huckleberry]

Good one. I think I've got it, also.

[johnnyshaka]

Turn on the lights???

[cuervo72]

I think I have it too, but in the back of my mind I feel like I heard/seen this somewhere in the last couple of weeks.

[Maple Leafs]

Got it too. Good puzzle. What's Car Talker?

[QuikSand]

Car Talk is a radio show on National Public Radio. Two hosts (brothers in real life) take calls from listeners who describe their car-related problems, and then dispense various advice. Sounds dreadful (to me, at least) but it's a real crack-up... the two hosts are real characters, and the show is extremely entrtaining (again, to me, at least).

They also do a puzzle every week... which is right up my alley, of course. When they did the "Monty Hall" puzzle they got inundated with hundreds and hundreds of cards and letters, and even set up their own web site as an experiment to help "prove" the correct answer to the legions of non-believers.

Car Talk Link (http://cartalk.cars.com/)

[KWhit]

Car talk is great. I know and care NOTHING about cars, but I listen anyway. It's that entertaining.


Still working on the puzzle, though...

[Radii]

I heard this episode while I was moving last week... great puzzle, but I must refrain from answering. And yeah, car talk is a great show.

[Passacaglia]

Car Talk is pretty fun. I don't listen to it that often, and also care nothing about cars, but it's always entertaining when I do happen to hear it.

[KevinNU7]

Ok I read their explanation and I still don't get it. It makes sense if they are all at the top but to me it doesn't if they are jumbled in the deck

[AnalBumCover]

OH! I got it.

[QuikSand]

Spoiler (for those who haven't searched for it):






Take ten cards from the deck, set them aside from the rest of the deck, and flip them over.

If none of the ten you set aside were face-up to begin with, then all ten of the face-ups were in the other stack. By turning over your stack of ten, you now have ten cards face-up in each stack.

If one of the original face-ups was in the ten you just flipped, then there are nine face-up cards in the other stack (all but one of the original ten) and now your stack of ten cards has nine face up.

...extend same logic to any other possible scenario...

If n of the original face-ups were in the ten you just flipped, then there are now 10-n face-up cards in the other stack (all but one of the original ten) and now your stack of ten cards has 10-n face up.