Would You Treat A Census-man This Way?

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A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are.

"I have three daughters, their ages are whole numbers, and the product of the ages is 36 36 ," says the mother.
"That's not enough information," responds the census-taker.
"I'd tell you the sum of their ages, but you'd still be stumped."
"I wish you'd tell me something more."
"Okay, my oldest daughter Annie likes dogs."

What is the age of the eldest daughter?

This problem is not original. \text{This problem is not original.}


The answer is 9.

Ameya Salankar by Ameya Salankar , 23, India

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3 solutions

Mohinder Goyal
Jul 24, 2014

Sum for 6,6,1 and 9,2,2 is same Product for both is 36 As only one daughter is eldest, so 2nd combination is the age of daughters.

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Sunil Pradhan
Aug 27, 2014

36 = 1 × 4 × 9

0 Helpful 0 Interesting 0 Brilliant 0 Confused

First break 36

36 = 2x2x3x3

36 = 4x3x3 OR

36 = 6x2x3 OR

36 = 2x2x9 OR

36 = 6x6x1

Try the biggest number in these combinations i.e. 9

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The answer can be 6 also. It is not mentioned that the biggest combination should be the answer.

Anuj Shikarkhane - 6 years, 10 months ago

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It's not "biggest combination should be the answer".Akshay's solution is not complete (and also misses out other combinations like 1 × 1 × 36 1 \times 1 \times 36 , which would have been a 'bigger' combination. Look at Mohinder's solution above.

The key step is to understand how to use "I'd tell you the sum of their ages, but you'd still be stumped". In particular, this means the ages cannot be 1, 1, 36, or 1, 2, 18, or 2, 3, 6.

Calvin Lin Staff - 6 years, 10 months ago

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