Question

A census taker approaches a house and asks the woman, "How many children do you have, and what are their ages?"

Woman: "I have three children. The product of their ages is 36, and the sum of their ages is equal to the house number of the house next door."

The census taker checks the house number, then says, "I need more information."

Woman: "My oldest child is sleeping upstairs."

What are the ages of the three children?

• A. 9, 2, 2
• B. 6, 6, 1
• C. 12, 3, 1
• D. 6, 3, 2

Hint:

Find product-36 triples whose sums tie (this is the ambiguous house number), then use "a single oldest child" to rule out the twin option.

Answer 1

The Correct Option is A

Instead of listing every possible triple with product 36, we can test the four given options directly against the two clues: the product must be 36, the sum must tie with at least one other product-36 triple (since the census taker needed more information despite knowing the house number), and there must be a single, uniquely oldest child.

1. 9, 2, 2: product = 9 x 2 x 2 = 36, correct. Sum = 13. Another triple, 6, 6, 1, also multiplies to 36 and sums to 13, so knowing the sum alone would genuinely leave the census taker stuck between these two, matching the "I need more information" line. This triple also has a single oldest child, the 9 year old, so the last clue confirms it.
2. 6, 6, 1: product = 6 x 6 x 1 = 36, and sum = 13, so this is the other member of the tied pair. But this triple has two children aged 6, so there is no single oldest child. The clue "my oldest child is sleeping upstairs" only makes sense if one child is unambiguously the eldest, so this triple is ruled out.
3. 12, 3, 1: product = 12 x 3 x 1 = 36, correct, but the sum is 16, and no other product-36 triple also sums to 16. The census taker would have solved the puzzle instantly from the house number alone, so this triple does not fit the "need more information" line.
4. 6, 3, 2: product = 6 x 3 x 2 = 36, correct, but the sum is 11, which again is not shared by any other product-36 triple, so this too would not have caused any confusion for the census taker.

Only 9, 2, 2 satisfies both the tie-in-sum requirement and the unique-oldest-child requirement, since its "twin" triple 6, 6, 1 fails the last clue.

Let's summarize:

• The product clue alone allows many triples, so it never pins down a unique answer by itself.
• The "still need more information" line tells us the sum must be shared by two triples.
• The "single oldest child" line breaks the tie by ruling out any triple with twins at the top.

The ages of the three children are 9, 2 and 2, which is option (A).