Long Lost Friends

11/22/2013

The following puzzle was sent to me by a friend. It's original source is unknown.

Two women meet after many years.

The first asks: "How old are your three daughters?"

The second woman says: "The product of their ages is 36."

First woman: "But that's not enough information."

Second woman :"Well, the sum of their ages is the same number as the room you and I shared in college."

First woman: "That still is not enough. "

Second woman: "The oldest one has blue eyes. "

First: "Thank you, now I know the girls' ages. "

What are the ages of the second woman's three daughters?

5 Comments

Cameron

3/24/2014 02:54:04 am

Three, Three, and Four.

Beth

10/26/2014 06:32:52 am

Can you explain how you got that answer? I'm having a hard time figuring out how to solve this riddle!

Mike

8/4/2016 07:17:04 pm

The solution can be arrived at by taking the statements and breaking them down 1 by 1.
Point 1 - Product of 3 (oldest being denoted as x, 2nd oldest y, youngest z) (x,y,z) = 36
Possible Solutions :
(1) x=18, y=2, z=1
(2) x=9, y=4, z = 1
(3) x=6, y = 6, z = 1
(4) x = 6, y = 3, z = 2
(5) x=4, y = 3, z = 3.

Step 2: Sum of the three STILL DOES NOT GIVE ENOUGH INFO TO SOLVE PROBLEM. In other words, sums that equal a unique solution are invalid, only sums that are equal to another solution might be valid:
Additive Sums:
(1) x+y+z = 21
(2) x+y+z = 14
(3) x+y+z = 13
(4) x+y+z = 13
(5) x+y+z = 11

Only solutions 3 and 4 are equal, therefor only one of the two could be correct.

Point 3: An apparently non-sequiter statement indicating the oldest has blue eyes. But this statement indicates that x cannot = y, as they would be the same age. The only remaining, and correct solution is option 4: The girls are 4,3,and 3.

Dennis Brewer

11/8/2017 02:37:57 pm

MIke's logic is spot on. The correct answer has a non-unique sum among possible answers with the two oldest not the same age. But for those reasons the solution is 9, 2, 2.

Cara

12/5/2017 10:29:46 am

You, Sir, are impressive. I was bamboozled by this (I am not a mathy), but your explanation was enough to make even me understand. Well done!

Long Lost Friends

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