Age of children
A (presumed smart) insurance agent knocks on a door and a (presumed smart) woman opens. He introduces himself and asks if she has any children. She answers: 3. When he then asks their ages (which for this problem we abstract to integers), she hesitates. Then she decides to give him some information about their ages, saying “the product of their ages is 36”. He asks for more information and she gives in, saying “the sum of their ages is equal to our neighbors’ house number”. The man jumps over the fence, inspects the house number, and the returns. “You need to give me another hint”, he begs. “Alright”, she says, “my oldest child plays the piano”. What are the ages of the children?
The answer is Ages 1, 1 and 36!
Clue 1 makes sure that all the possible ages must have a product of 36. Many threads below have the right idea.
Clue 2 ensures that next door (always either+2 or -2) from your own number. Therefore the sum of the ages must be either +2 or -2 from the product. The only combination possible is 1, 1 & 36 with a product of 36 and a sum of 38.
Clue 3 cannot see the need for it! (But at 36 you could still be learning the piano!)
Youngest |
Middle |
Eldest |
Product |
Sum |
Diff |
1 |
1 |
36 |
36 |
38 |
2 |
1 |
2 |
18 |
36 |
21 |
-15 |
1 |
3 |
12 |
36 |
16 |
-20 |
1 |
4 |
9 |
36 |
14 |
-22 |
1 |
6 |
6 |
36 |
13 |
-23 |
2 |
2 |
9 |
36 |
13 |
-23 |
2 |
3 |
6 |
36 |
11 |
-25 |
2 |
3 |
6 |
36 |
11 |
-25 |
There is no indication that the house number is the same as the product. The reason he asks for more hint is that both 2,2,9 and 1,6,6 fit the first two clues. The fact that there exists an eldest implies that 2,2,9 must be the ages of the children.
Answer is 2, 2, 9
Clue 1: The product of ages is 36. So possible answers are 1 1 36, 1 2 18, 1 3 12, 1 4 9, 1 6 6, 2 2 9 and 2 3 6
Clue 2: The sum of ages is equal to neighbor’s house number. The sum of above is 38, 21, 16, 14, 13, 13, 11
After these 2 clues, the ages could not be determined if the product and sum of ages are same. So only 2 groups left – 1 6 6, 2 2 9.
Clue 3: The oldest child plays the piano. means 1 6 6 is eliminated and only 2 2 9 is left
Your Answer
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