Puzzle Lab / Logic Puzzles
The Blindfolded Cards
A clean invariant puzzle: split cards while blindfolded so both piles have the same number of face-up cards.
Puzzle
Challenge first.
A table has many cards. Exactly 10 are face up. You are blindfolded, and you can flip cards but cannot tell which side is up. How can you create two piles with the same number of face-up cards?
Hints
- You do not need to know which 10 cards are face up.
- Try making one pile with exactly 10 cards.
- What happens if you flip every card in that pile?
Solution
Take any 10 cards and put them in one pile. Flip every card in that pile. If that pile originally had k face-up cards, the other pile had 10 - k face-up cards. After flipping, the 10-card pile also has 10 - k face-up cards.