The Puzzle: A blind man has to take two types of medication, Pill A and Pill B, every day.
- He must take exactly one of Pill A and exactly one of Pill B.
- He has 4 pills in total: two of A and two of B.
- However, they all look and feel identical. He accidentally mixed them up. How can he ensure he takes exactly one of each pill without any help?
1. The Strategy: Symmetry
Since he cannot identify the pills by sight or touch, he must use division.
- Cut every pill in half.
- Create two piles: Pile 1 and Pile 2.
- For each of the 4 pills, put one half in Pile 1 and the other half in Pile 2.
- Each pile now contains: Half of A1, Half of A2, Half of B1, and Half of B2.
- Taking any one pile is mathematically equivalent to taking:
- (Half A + Half A) = 1 Full Pill A
- (Half B + Half B) = 1 Full Pill B
2. Result
By dividing everything symmetrically, he consumes the correct dosage regardless of which physical pill was which.
Interview-Focused Questions
Q: Does this work if the pills are different shapes?
A: If they were different shapes, he wouldn’t be in this mess because he could feel the difference! The puzzle assumes they are identical in every physical way sensible to a blind person.
Q: Could he crush them all into a powder instead?
A: Theoretically, yes. If he crushes all 4 into a powder, mixes it perfectly, and takes exactly half of the powder, he also gets the right dose. However, cutting them in half is much more practical and less messy.
Key Takeaway
When you can’t distinguish between items, treat them as a collective pool and divide the pool.
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