Blindfolded: split a deck of cards so they have the same number of face up cards

[[leetcode]]

Problem

1. You're blindfolded
2. You have a deck of cards
3. 13 cards are randomly face up
   1. 39 cards face down

Goal

• have 2 piles of cards such that each pile has the same number of face up cards

What can we do?

Operations

• I can flip a card from face up to face down or vice-versa
  • I don't know which one I'm actually doing
• I can somehow divide the cards into groups
  • because I don't know anything about the cards individually, I will only lose information if I split them up
  • so I likely have to do one split to not lose information

Brute force attempts

Pile A: 1 card and pile B with 51 cards in the other

• possible result: 0-1 in pile A and 13 or 12 in pile B

Pile A: 2 cards, pile B: 50 cards

• 0, 1 or 2 in pile A and 13, 12, 11 in pile B

Pile A: 13 cards, pile B: 39 cards

• 0, ..., 13 in pile A and 13, … 0 in pile B

If I were to take 13 random cards and flip them in pile A

• if there were 0 face up cards originally pile A
  • after we flip, there would be 13 in pile A
  • the same number as Pile B
• if there were 1 face up card …
  • the same number as Pile B

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Last update: 2023-04-24