Coins (Blindfolded)
The Puzzle: You are in a dark room with 100 coins.
- Exactly 10 coins are Heads up.
- Exactly 90 coins are Tails up.
- You are blindfolded and cannot feel the difference between head and tail. How can you divide the coins into two groups such that both groups have the exact same number of Heads?
1. The Strategy
The solution is surprisingly simple but counter-intuitive.
- Pick any 10 coins and put them in Group A.
- The remaining 90 coins go in Group B.
- Flip every single coin in Group A.
2. The Proof
Let’s say in the 10 coins you picked, X were Heads.
- In Group A, you now have X Heads and (10−X) Tails.
- In Group B, there are (10−X) Heads remaining (since the total Heads was 10).
- When you flip all 10 coins in Group A, the X Heads become Tails, and the (10−X) Tails become Heads.
- Result: Both groups now have exactly 10−X Heads!
Interview-Focused Questions
Q: Why does this work regardless of how many heads I pick?
A: Because you chose the size of the first group to be equal to the total number of heads in the system. This creates a inverse relationship that is perfectly corrected by flipping the whole group.
Q: Does it matter if I pick 20 coins instead?
A: Yes. To make the math work, the size of the smaller group must be equal to the total number of heads initially present in the set.
Key Takeaway
This is a puzzle about Parity and Inversion. It shows how a simple transformation (flipping) can solve a problem that seems to require vision/sensing.
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