The eyes are blue

Level 2

A man bumps into his mathematician friend on the street that he hasn't seen in 5 years. The man asks the mathematician how old his children are. The mathematician who always replies in riddles said "I now have three children. The sum of their ages is equal to the number of windows on the building in front of you and the product of their ages equals 36." The friend then says "I need one more piece of information." The mathematician then replies "My youngest child has blue eyes." What is the number of windows in that building

The answer is 13.

3 solutions

Noel Lo
May 17, 2015

Let the three children's ages be $a, b, c$ where $abc = 36$ . $a+b+c$ = no. of windows. This number of windows seen must have more than one possibility of $a, b, c$ values satisfying $abc = 36$ such that the man has to ask for another piece of information.In fact, for one of the possibilities, there must be two smallest values and for the other possibility, there must be exactly one smallest value such that there is a youngest child. The answer is $\boxed{13}$ such that the 2 possibilities are $(a, b, c) = (9, 2, 2)$ and $(a, b, c) = (6, 6, 1)$

Why couldn't the children's ages be 2,3,6?

G Silb - 1 year ago

The fact that the mathematician hint only for the "youngest" child makes it clear ,the answer is $6,6,1$ . And NOT $9,2,2$ ,dont be misleaded by confusion created by noel, I request you to edit your solution, noel.

Siddharth Bhatnagar - 6 years ago

Siddharth Bhatnagar
May 16, 2015

The children are $6,6,1$ year old

How do you come to this solution? What was your thinking when you arrived at this solution?

Taran Kota - 6 years ago

Hi,Its not that hard you see. First list out the possible ages keeping in mind that youngest child is less than five years and other two are greater than five years(think for yourself,why would mathematician tell that his youngest son has blue eyes, its because his friend had not seen this child of him, or else he would have already known that there is a child that has blue eyes. ) Lets list

{Youngest child,other child#1,other child#2}

{1,6,6}

{2,3,6}

{2,9,2}

{2,2,9}

{1,4,9}

{2,18,1}

{3,4,3}

{3,3,4}

{4,3,3}

Clearly {1,6,6} is the only way that matches constraints.

Siddharth Bhatnagar - 6 years ago

Ah, ok. Thanks for showing me!

Taran Kota - 6 years ago

@Taran Kota – :) thanks to you!

Siddharth Bhatnagar - 6 years ago

Chen Albert
Jun 2, 2020

36+1+1=38 18+2+1=21 9+4+1=14 9+2+2=13 3+6+2=11 1+6+6 =13 3+3+4=10

He says he needs one more information means there are two sum are same and the Mathematician says he has youngest Child,therefore the answer is 1,6,6

The eyes are blue

The answer is 13.

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