['Cat'astrophe]

Kat was travelling in a train and she was getting kind of bored. The passenger oppposite her was a math professor and they had chatted for some time but he was just rambling on.

"Looks like i'm boring you", said the profeesor,"so how about a puzzle? First tell me your age."

Kat thought this to be rather impolite but told him her age.

The professor resumed, "I know three people. The sum of their ages is equal to your age. The product of their ages is 2450. Can you tell me their ages?"

Kat thought for a while and declared, "It's not possible to solve this."

The professor said,"I know. But if I tell you that I am younger than the oldest of them, you will be able to tell me their ages as well as mine."

What is the professor's age?

[CaptainEd]

The prime decomposition of 2450 is 2, 5, 5, 7, 7

The possible combinations of 3 ages and their sum are

2 + 5 + 245 = 252 (ageless indeed!)

2 + 7 + 175 = 184

2 + 25 + 49 = 76

2 + 35 + 35 = 72

5 + 5 + 98 = 108

5 + 7 + 70 = 82

5 + 10 + 49 = 64

5 + 14 + 35 = 54

7 + 7 + 50 = 64

7 + 10 + 35 = 52

7 + 14 + 25 = 46

The only age that Kat could not solve would be 64, because it has two solutions, so her age is 64.

But between 5 ,10 ,49 and 7, 7, 50, how do we know whether the professor is younger than 49 or 50? There's some delicious gimmick I am not seeing.

Edited August 17, 2011 by CaptainEd

[Guest]

The Product of their ages is 2450 (a x b x c = 2450)

as this ends in a zero, one must be 10, or 50 or 70 ( the only multiples of 10 that are factors of 2450)

Divide these into 2450 gives 245, 49 and 35

The only possible alternatives for the three ages are therefore,

70,35,1

70,7,5

50,49,1

50,7,7,

10,49,5

10,35,7

I am guessing the professor is 49 from the number combination 50,49,1, which would make Kat 100 years old, quite age-less....

Or the other option would be that he is 35 , then Kat would be 106 years old....

Edited August 17, 2011 by BusyMom

[Guest]

The prime decomposition of 2450 is 2, 5, 5, 7, 7

The possible combinations of 3 ages and their sum are

2 + 5 + 245 = 252 (ageless indeed!)

2 + 7 + 175 = 184

2 + 25 + 49 = 76

2 + 35 + 35 = 72

5 + 5 + 98 = 108

5 + 7 + 70 = 82

5 + 10 + 49 = 64

5 + 14 + 35 = 54

7 + 7 + 50 = 64

7 + 10 + 35 = 52

7 + 14 + 25 = 46

The only age that Kat could not solve would be 64, because it has two solutions, so her age is 64.

But between 5 ,10 ,49 and 7, 7, 50, how do we know whether the professor is younger than 49 or 50? There's some delicious gimmick I am not seeing.

We can have some more combination (as you forgot a factor 1):

2450+1+1 = 2452

1225+1+2 = 1228

490+1+5 = 496

350+1+7 = 358

245+1+10 = 256

175+1+14 = 190

98+1+25 = 124

70+1+35 = 106

50+1+49 = 100

But the problem remains same: Who is oldest? And how much younger is the professor?

My guess is the professor is 49 years old and that's why he is saying that a definite answer can be reached by knowing he is younger to oldest man (50 years of 50, 7, 7 combination). If we make him more younger (48 or less), both answer will remain valid (50,7,7 and 49,5,10) and his statement will become wrong.

Hence my answer: Professor is of 49 years and Kat is of 64 years.

['Cat'astrophe]

Swapnil is correct..with Ed getting the first bit of the puzzle. .

Kat could not say their ages definitively since there were two combinations 50,7,7 and 49,10,5 for her age 64.

Swapnil's logic is perfect for determining their ages.

[Guest]

:D :D :D :D

[CaptainEd]

Oh, yeah, a prime number is one that is divisible only by itself and...and...uh...that other thing...

[Guest]

We can have some more combination (as you forgot a factor 1):

2450+1+1 = 2452

1225+1+2 = 1228

490+1+5 = 496

350+1+7 = 358

245+1+10 = 256

175+1+14 = 190

98+1+25 = 124

70+1+35 = 106

50+1+49 = 100

But the problem remains same: Who is oldest? And how much younger is the professor?

My guess is the professor is 49 years old and that's why he is saying that a definite answer can be reached by knowing he is younger to oldest man (50 years of 50, 7, 7 combination). If we make him more younger (48 or less), both answer will remain valid (50,7,7 and 49,5,10) and his statement will become wrong.

Hence my answer: Professor is of 49 years and Kat is of 64 years.

I understand your reasoning but I don't get why when you are saying the professor is 49 , which means you are using the combination ( 50,49,1= sum of 100) you still say that Kat is 64 even though it would mean that she is 100.

[Guest]

@busymom

no... I think swapnil is using the combination of 50 7 7..

u cannot use the combination of 50 49 1 because if u use that combination.. Kate would have gotten the answer before the professor gave him any clue..

since Kate is confused.. we can tell that her age is 64 years old..

since there are two combinations that is confusing Kate.. and that is 50 7 7 and 49 10 5

if we use the combination 49 10 5

the professor would have to be 48 years old or less.. which both the combination 50 7 7 and 49 10 5 would be correct.. Thus the statement of the professor that it can be solved would be wrong...

so the combination have to be 50 7 7

which means that the professor has to be 49 years old or less.. and again.. he cannot be 48 years old or less.. which suggest that the profesor has to be.. 49 years old.