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

Posted August 31, 2023 12:00 AM
Pathfinder Tags: challenge question

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.

• You must organize the cards into two piles.
• Each with the same number of face up cards.
• You are allowed to flip cards over as needed.

How do you proceed?

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### Comments rated to be Good Answers:

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3
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#1

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

08/31/2023 3:08 AM

Take 20 cards from the deck and form a pile, what cards are left will be the second pile...turn the first pile over...the 2 piles now have an equal number of face up cards...

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Good Answer (Score 3)
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#2
In reply to #1

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

08/31/2023 8:56 AM

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.

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#7
In reply to #1

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

09/05/2023 9:00 AM

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?

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vsar
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#8
In reply to #7

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

09/05/2023 10:35 AM

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.

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#9
In reply to #8

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

09/05/2023 11:47 AM

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..

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#10
In reply to #9

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

09/05/2023 12:45 PM

Friend,

SE is correct, although it is not obvious. The key to this is that the pile you will work with has the same number of random cards in it as the total that were face-up mixed in the whole deck.

Assume your pile of 20 has 4 that were face up, that means that 16 are face up in the remaining pile. By turning all your cards the other way, the 4 that were face up are now face down while the 16 that were face down are now face up. You then have 16 face up cards in both piles. Note that the total number of face up cards has changed from 20 to 32, but that doesn't matter.

This same approach works regardless of the initial number of face up cards. You just put into your first pile the same number of cards as the total that were face up at the start.

JMM

Good Answer (Score 3)
Anonymous Poster #1
#12
In reply to #10

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

09/25/2023 3:06 PM

Explains it better than admin can. Bravo!

Anonymous Poster #1
#11
In reply to #1

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

09/25/2023 3:06 PM

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

@jmueller gives a great rundown in reply #10.

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#3

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

09/01/2023 9:24 AM

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...

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#4

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

09/01/2023 6:03 PM

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

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#5
In reply to #4

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

09/05/2023 5:12 AM

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...

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#6
In reply to #5

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

09/05/2023 8:07 AM

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

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#13

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

10/04/2023 9:51 PM

Turn on the light.

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