Interview Questions And Answers 
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Two MIT math graduates bump into each other. They hadn’t seen each other in over 20 years.
The first grad says to the second: “how have you been?”
Second: “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.. hmmmm.., I still don’t know”
second: “Oh sorry, the oldest one just started to play the piano”
First: “Wonderful! my oldest is the same age!”Problem: How old are the daughters?
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8, 3, 3.
Your need to find two groups of 3 numbers such that their product is 72 and the sum is the same.
In this case, it is 8, 3, 3 and 6, 6, 2.
And with the second condition, we can infer that the first one is the answer.
Yap, these kind of things are called Diophanine Equations…with multiple solutions, but some solutions are rejected on practiciality.
Actually the solutions create a part of the surface in the Manifold.
I would have assumed the ages: 9, 4, 2.
(9 * 4 * 2) = 72
The examples you provided consisted of twins ( 6, 6 ) and ( 3, 3 ). The possibility of having 3 daughters of different ages is more probable than having twins.
#4 is incorrect. It is not an issue of probabilities. person #1 knows the number on the building. Now this means that there must be some ambiguity even if he knows both the sum and product. Thus (9,4,2) is invalid, as are most other solutions. We need a sum that can be formed in two ways. 14 is the only such sum (8,3,3) and (6,6,2). Now identifying one as the oldest means that twins for the oldest are impossible. Therefore (8,3,3) is the only possibility.
There exists persons like Plagueis (read above) who will not give the solutions but will talk like (sorry will type like) Einstein.
Anyways, Rebsky (#5) has given the correct explanation.
More easily, to find a exact solution for 3 unknows you need 3 equations, but here we have two equations, sum and product which is a*b*c=72 and a + b + c = n. Therefore for these two equations to be solvable we should decrease the number of unknows, and accept that two child has the same age. a * b * b = 72, a + b + b = n . If we make this acceptance we should find a squared number times a number makes 72, thats 9 * 8 (3,3,8) or 36 * 2 (6,6,2) , and accepting that one is the oldest, we can say 3,3,8 is the only correct solution
The possible solutions are (12,3,2), (9,4,2), (6,4,3), (9,8,1)
- The oldest can not be more than 20 years old since the have not seen each other for 20 years.
- What matters is their product only.
- The second condition about their sum is not needed.
- The third one is need, so depending on at what age can a kid play piano, we determine the solutions accordingly. For me I think at age 6, which leaves me with (6,4,3)
(8,3,3) & (6,6,2) are the two possibilities which produce the same product and sum. Which was why the mathematician was confused. In second case two elder kids are of same age, so you cannot pick an “oldest”. Answer is (8,3,3) hence.
Also isn’t eight is the age kids start to learn Piano ?
I agree that 8, 3, 3 was probably the solution the problem’s creator had in mind … however, there is a flaw in the reasoning.
A twin can be the oldest … one twin is always born first. There should have been some other hint to differentiate between 8,3,3 and 6,6,2.
It is also conceivable for 2 of the daughters to be the same age, not twins, and one be older than the other … born, say, January and November … they would be the same age in November and December of every year … and,of course, one would be older than the other.
This may have been a better problem.
· Two MIT math graduates, Mike and Bob, bump into each other. They hadn’t seen each other in over 25 years.
Mike says to Bob, “How have you been?”
Bob: “Great! I got married and I have three daughters now”
Mike: “Really? How old are they?”
Bob: “Let’s see if you still have the magic you had in college. The product of their ages is 72 and the sum of their ages is the same as the number on that building over there.”
Mike: “Right, ok … well you haven’t given me enough information.”
Bob: “Oh, you’re right, sorry … the product of my youngest and my oldest is 4 less than a perfect number.”
Mike: “Wonderful, my oldest is the same age!”
How old are the daughters?
Richard,
I agree with you but wouldn’t it complicate the answer as the person may not know what a perfect number is.He could have as well said. “The number on that building is the same as the difference between the highest and lowest age among my daughters.” Or the product of ages of my youngest and oldest daughers is just 1 lesser than a perfect square. For that matter, there are umpteen ways of pointing to 3,3,8 over 6,6,2.
Anyhow nice catch Richard. I appreciate your keenness.
What if their ages are 12,3,2 is it so extraordinary to have 10 years difference between sisters, I suppose you came across with people who has this much age difference between their brother or sisters ? So, why everybody counts out this possibility ?
How about 18, 2, 2 OR 72, 1, 1?
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