A Deck of Cards in the Dark (September '23 Challenge Question)

Very clever...

Of 20 cards removed from the deck, n will be face up, (20 - n) will be face down, and there will be (20 - n) face-up cards left in the deck. Turning the removed cards over reverses the (20 - n) face-down cards to face-up, matching the (20 - n) face-up cards left in the deck.

SolarEagle - If you are not able to see the cards being dark in the room. I'm wondering how you determine which cards are faced up among the shuffled cards on the table?

You don't need to be able to see them.

First for clarity: I'm going to er-state part of the question.

The controller takes a full deck of cards turns 20 of them the opposite way up from the rest then shuffles them thoroughly, and, places them in the darkened room.

To achieve your goal you simply take the top (or any) twenty cards and turn them the other way up.

Understood that it was a given:

You are in a very dark room where you cannot see anything.

You are given a shuffled deck of cards. Additionally, 20 cards are arranged face up; the rest are face down.

If the cards were preshuffled then

How would anyone identify which ones are already facing up?? amongst the preshuffled..

Explains it better than admin can. Bravo!

Correctomundo! Although it doesn't have to be 20. Any number would work.

@jmueller gives a great rundown in reply #10.

Grab any of the two piles of cards on the table then flip the whole pile of cards that are in your hand a put the pile back on top of the other untouched pile left on the table..

Now you will have just one combined pile of cards that are all facing either up or down on the table.. Start splitting the pile by just sliding the cards to one side until the top of the two resulting piles of cards are even and equal...

The resulting two even height of piles of cards on the table should be all sharing the same orientation and facing the same way, either face up or facedown...

It appears that the answers assume that the first 20 cards are face up, or some similar assumption. However, if they are randomly located in the deck, the problem becomes one of the very slightly different feel of the front or back of the cards.

Have fun with figuring it out.

--JMM

No, the face up cards can be randomly located, and the cards drawn to make the first pile can be randomly selected, the key is knowing the number of face up cards to begin with....try it, you'll see the two piles always come out even...it's a neat trick to be sure, but really simple once you see how it works...

Wow. It appears to me that one can do this with other quantities of face-up cards. Just form your first pile with the same number of cards in it (such as 12 if there were 12 face-up cards, etc.), randomly selected as you said.

--JMM

Turn on the light.