Logic Puzzles and Brainteasers

The Census Taker Problem

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

The woman replies "I have three children, the product of their ages are 36, the sum of their ages are equal to the address of the house next door."

The census taker walks next door, comes back and says "I need more information."

The woman replies "I have to go, my oldest child is sleeping upstairs."

Census taker then says "Thank you, I now have everything I need."

At first sight, this problem seems inpenetratable. How in the world are the second and third reply of the woman going to help us? It turns out that they're the key of determining the answer.

The product of the ages is $36$, so there are few possibilities :

$1, 1, 36$ Sum : $38$

$1, 2, 18$ Sum : $21$

$1, 3, 12$ Sum : $16$

$1, 4, 9$ Sum : $14$

$1, 6, 6$ Sum : $13$

$2, 2, 9$ Sum : $13$

$2, 3, 6$ Sum : $11$

$3, 3, 4$ Sum : $10$

Try to solve the problem from here. Click Continue when you're ready for the next part of the solution.

Now we know what the second reply means! Since the census taker still can't determine their ages after knowing the sum, it follows that the sum must be $13$, so that there could be ambiguity. The last statement states that the oldest child exist, so the ages must be $2, 2, 9$!

Puzzle Your Logic! Tease your Brain!

Test your knowledge of probability and statistics with these challenging problems to test your solving skills in fun, clever, and unique ways!