Is that enough? really?

Number Theory Level 3

- Peter, how old are your children? - Well Thomas, there are three of them and the product of their ages is 36. - That is not enough ... - The sum of their ages is exactly the number of beers we have drunk today. - That is still not enough. - OK, the last thing is that my oldest child wears a green cap.

How old were each of Peter's children?

If the ages of his children are $a \leq b \leq c$ , then enter your answer as $abc$ .

The answer is 229.

2 solutions

Rishabh Nishad
Mar 4, 2014

There are two possible combinations with the same sum (1-6-6 a 2-2-9). And as we learned further that the oldest son wears a cap, it is clear that the correct combination of ages is 2-2-9, where there is exactly one of them the oldest one

what about the combinations 2-3-6,1-4-12,1-4-9 and 3-3-4? how did you rule them out???

Swapnil Man Joshi - 7 years, 3 months ago

The other combinations have different sums. Since he didn't have enough information, it meant it had to be a combination with the same sum.

Sharky Kesa - 7 years, 1 month ago

Agnishom Chattopadhyay
Mar 3, 2014

Look at hint 2 -> Since one can drink only integer number of beers, the ages of the children are integers

Look at hint 3 -> It says that there exists an oldest child.

There is only one integer triplet that satisfies all three conditions (2,2,9)

334 , 149 ,236 also satisfy all three conditions given

venkateswari s - 7 years, 3 months ago

yeah !! but sum should be equal too(no. of drinks) 2+3+6=11 1+4+9=14 3+3+4=10 so u have to find such combinations which will give the same sum as well ,

Deepali Kemwal - 7 years, 3 months ago

The Problem is saying that "The sum of their ages is exactly the number of beers we have drunk today." How you find out no of beers they have drunk?

venkateswari s - 7 years, 3 months ago

@Venkateswari S – see ! you'll be getting many combinations like 334 , 149 ,236,1-4-12,1-6-6 , 2-2-9 ok? among these you'll have to select the combinations in which the no.s have their sum equal too because whatever may be the number, they drank a particular number of beers. so there are 2 combinations who have their sums equal (229,166)

Deepali Kemwal - 7 years, 3 months ago

@Deepali Kemwal – you are seriously a fool .There is no clue about noumbers of beers! it may be 11, 14, 10 or 13! each number correspondes to different set where the no. 13 correspond to two set (229) and (166). From where did you get the condition that two combination should have same sum? Do you go to school? This question has 4 answers i.e (229,149,334,236). Your hint 3 that 1 of them is oldest rules out (166).

Gaurav Kukreja - 7 years, 2 months ago

@Deepali Kemwal – "among these you'll have to select the combinations in which the no.s have their sum equal too because whatever may be the number, they drank a particular number of beers." ---- where this condition is mentioned in questions?

venkateswari s - 7 years, 3 months ago

@Venkateswari S – c'mon thats common sense !! i am done ! i cant explain it any further ! sorry !! i am a very BAD teacher !!

Deepali Kemwal - 7 years, 3 months ago

@Deepali Kemwal – I think this contradict the combinatoric formula(double counting) in which you states "The sum of their ages ia exactly the number of beers WE drunk today." By double counting: if the number of beers is x, by double counting we means 2 people means x must be even and the sum of2,2,9 and1,6,6 is odd. But the explanation that because there are 2 combinations that have the same sum is right.

Samuel Samuel - 6 years, 5 months ago

@Venkateswari S – The person who is asking the question to Peter knows the number of beers they had drunken, even then he was not able to answer the question after the second hint, this can only be possible if there exist 2 combinations which have their sum same......... and those combinations are - (6, 6, 1) and (2, 2, 9). But the third hint states that there is a eldest child so the answer is 229. Hope you have understood now.

Aman Bansal - 7 years, 2 months ago

This question is cheated from somewhere. I don't remember.

Satvik Golechha - 7 years, 3 months ago

actually it is !! :) cuz i cannot make my own questions , like you guys do !! maybe !!

Deepali Kemwal - 7 years, 3 months ago

But still, Deepali, you should write the source below the question in italics

Satvik Golechha - 7 years, 3 months ago

@Satvik Golechha – yeah you're right !! i' ll definately do that next time !

Deepali Kemwal - 7 years, 3 months ago

You should have written the question moreaccurately.

Aashish Patel - 7 years, 2 months ago

Is that enough? really?

The answer is 229.

2 solutions

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