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Splitting a deck of cards into 2 piles Question
A blind person is handed a deck of 52 playing cards and told that exactly 10 of these cards are facing up. How can they divide the cards into two piles, not necessarily of equal size, with each pile having the same number of cards facing up?
1 answer
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | Apr 10, 2026 at 04:14 |
I don't mean to be flippant but this is actually pretty straightforward.
Of the top 10 cards (really any arbitrary 10-card subset, but this is simplest), suppose N are facing up; since 10 total cards are facing up, the rest of the deck has 10-N cards facing up — all of the face-up cards except for the ones in the top part.
So, let us simply take those 10 cards and turn them upside-down, thus flipping each card. Since N were facing up beforehand, now 10-N are facing up — all of them except for the ones that were before.
Now there are 10-N face-up cards among the flipped cards (the first pile), and the rest of the deck (the second pile) also has 10-N face-up cards, meeting the condition.
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