Question 765059: 3. Two mathematician graduates bump into each other while shopping at Vishal’s. They haven't seen each other in over 20 years.
The first graduate says to the second: "How have you been?"
The second replies: "Great! I got married and I have three daughters now." First: "Really? How old are they?"
Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
First: "Right, ok... Oh wait... Hmm, I still don't know."
Second: "Oh sorry, the oldest one just started to play the piano." First: "Wonderful! My oldest child is the same age!"
how old was the first graduates child?
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website!
Product of ages is 72. Sum is the number on the building
We try the possible combinations of the product of ages and also the corresponding
sum.
72,1,1 - sum = 74
36,2,1 - sum = 39
18,2,2 - sum = 22
18,4,1 - sum = 23
9,8,1 - sum = 18
9,4,2 - sum = 15
8,3,3 - sum = 14
6,6,2 - sum = 14
Now here's the trick. The 2nd mathematician was NOT able to guess the ages
even after checking the sum. From the table above, you see that all the possible
combinations have unique sums except (9,4,2) and (8,3,3) which have the same
sum. So the door number must be 14 and the mathematician is still not able to
find which is the right combination.
3rd clue refers to "oldest" child which means that (6,6,2) is not possible -
because there are 2 children with the same age of 6 and you can't refer to one
as the "oldest".
Hence the right combination is (8,3,3)
The ages are 8, 3 and 3.
:)
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