The Puzzle: Two friends meet. One says: “I have 3 daughters. The product of their ages is 72, and the sum of their ages is the same as the number on that house across the street.” The second friend looks at the house and says: “I still don’t know their ages.” The first friend adds: “The oldest one likes strawberry ice cream.” What are the ages?
1. The Possibilities
The product is 72. Let’s list the combinations (x,y,z) and their sums:
| Ages | Sum |
|---|---|
| (1, 1, 72) | 74 |
| (1, 2, 36) | 39 |
| (1, 3, 24) | 28 |
| (1, 4, 18) | 23 |
| (1, 6, 12) | 19 |
| (1, 8, 9) | 18 |
| (2, 2, 18) | 22 |
| (2, 3, 12) | 17 |
| (2, 4, 9) | 15 |
| (2, 6, 6) | 14 |
| (3, 3, 8) | 14 |
| (3, 4, 6) | 13 |
2. The Deduction
- Friend 2 knows the house number, yet says “I still don’t know.”
- This means the house number must be a sum that appears twice in our list.
- The house number is 14. The possibilities are (2, 6, 6) and (3, 3, 8).
3. The Clue
- “The oldest one likes strawberry ice cream.”
- This implies there is a single oldest daughter.
- In the case (2, 6, 6), there are two 6-year-old “oldest” twins.
- Therefore, the ages must be 3, 3, and 8.
Interview-Focused Questions
Q: Why do we care about the house number if we don’t know what it is?
A: Because the friend does know it. If the house number was 13, the friend would have known the ages immediately (3,4,6). The fact that he was confused proves that the sum was 14.
Q: What if the oldest one liked chocolate instead?
A: The flavor of ice cream is a “distractor”. The only informative part of that sentence is the word “oldest” (singular), which allows us to differentiate between (2,6,6) and (3,3,8).
Key Takeaway
This is a classic “Constraint Satisfaction” puzzle. It’s about finding the one set of variables that satisfies every piece of information provided, especially the “negative” information (the confusion of the friend).
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