The Blindfolded Cards
A clean invariant puzzle: split cards while blindfolded so both piles have the same number of face-up cards.
You cannot see the cards. You still need to make two piles with equal face-up cards.
Puzzle
Try it before the answer.
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.
See The Invariant
The trick is not eyesight. The trick is choosing a pile whose size matches the hidden count, then flipping the question around.