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### Popular Age Problem

Popular Age Problem - 27 july

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.

How old are Bill’s kids?

1. Why Not 6,4,3

2. Amswer might be 2,4,9

2. Why not 1 6 12 ?

1. yah i think

2. Hey Anonymous! Your wrong! It is 72

3. hahahaha how do you correct someone, but you're wrong

4. hahahaha how do you correct someone, but you're wrong

3. why not 3, 4, 6

1. sum=13, jack cant be 13

2. The sum is Jack's birth date. Not his age.

4. 3, 3, 8

why because.. the sum is ambigous though sum of the ages is the same as Jack's birthdate... it means the ages are either 2, 6, 6 and 3, 3, 8.. sum of both combinations is 14.. now there is an elder son.. so answer must be 3, 3, 8

1. i think it may be 2.4,9 i dont they are of same ages

2. its 2, 12 , 3

3. who says that his birthdate is 14

4. 1. Birthday is 14 because it is the only birthday that doesn't give a solution without further information

2. Why assume it's a son? Not given :(

5. a kid of age 6 can go to piano class so I think 3,4,6 would be a most agreeing solution

6. Could be 2,6,6. Even if eldest two are twins, one was born first, and therefore 'the eldest kid'

5. why can't it be 2,4 & 9

1. because he couldn't answer until he knew there was an elder guy, so we can take all the numbers that their product is 72 and sum them, then we need to take the ones that give the same answer (3-3-8 & 2-6-6) each one gives 14 noa, we know there's an elder so... tha answer is 3-3-8 got it?

6. But where is given that jack's age is 14???

I think 3 3 8 is right choice.
because general age after which we can take piano lesson is 8 thats why.....

1. jack's birth date is 14.

7. 9,7,2 respectively..:)

1. They need to equal 72.
9x7=63. 63x2=126. It can't be 9,7, and 2.

8. why can't it be 2,2 and18?

1. see the sum of all ages is different for all cases except 3,3,8 and 2,6,6 in which case it is 14. and he was confused till he came to know that there is one elder son. so 3,3,8 is the right answer

9. The product of their ages is 72. So what are the possible choices?

2, 2, 18 – sum(2, 2, 18) = 22
2, 4, 9 – sum(2, 4, 9) = 15
2, 6, 6 – sum(2, 6, 6) = 14
2, 3, 12 – sum(2, 3, 12) = 17
3, 4, 6 – sum(3, 4, 6) = 13
3, 3, 8 – sum(3, 3, 8 ) = 14
1, 8, 9 – sum(1,8,9) = 18
1, 3, 24 – sum(1, 3, 24) = 28
1, 4, 18 – sum(1, 4, 18) = 23
1, 2, 36 – sum(1, 2, 36) = 39
1, 6, 12 – sum(1, 6, 12) = 19

The sum of their ages is the same as your birth date. That could be anything from 1 to 31 but the fact that Jack was unable to find out the ages, it means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.

2, 6, 6 – sum(2, 6, 6) = 14
3, 3, 8 – sum(3, 3, 8 ) = 14

Since the eldest kid is taking piano lessons, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8.

1. perfect ans

2. its damn true

3. what is the relation with jack age which is not mentioned here.and what is the link with piano class..plz make me understand

4. let's see the explanation above. there we can see several possible numbers that can give a product of 72.

now comes the birthday factor.

"Bill: sum of their ages is the same as your birth date"

"Jack: Cool… But I still don’t know."

Jack don't know because more than one possible combination give the sum similar to his birth date. now look through the possible combinations, you will only get the result 14 occurring twice. so, Jack's birth date is 14. but the question still remains, which is the right combination?

that's where the piano lesson comes in action. only one kid started piano lesson, so one kid is older. now look at both combinations, see which one has unique greater number.

2, 6, 6 – sum(2, 6, 6) = 14
3, 3, 8 – sum(3, 3, 8 ) = 14

we can see that first one has 6 occurring twice which is larger number of that combination, but we know that only one kid is older; so we have the second combination where 8 is unique larger number.

6. well duh its well explain he just copied it from the answer page.

7. Perfact Explanation

8. you explained it very well, 3,3,8. anyone having doubt after reading this explanation is dump.

9. The reason they talk about piano lessons is because there are eight keys in an octave so 8 has to be part of the answer

10. No, it's so they could use 'eldest'. Look up the difference between 'oldest' and 'eldest'

11. Even with twins, one of them is "older", if just by a minute or two - if somebody wanted to get picky!

1. you don't know; its number

11. The eldest son should have started the piano lessons earlier

12. It don't make sense to me It is too hard hehehe

13. 9, 4, and 4. It's easy, what is 9x8? 72. Because he said product.

1. The product of 9,4 and 4 is 9 x 4 x 4 = 144

15. 12, 3, 2 one child is taking piono lessons means other two are not capable yet ie 3 & 2 years old

16. I think I am missing something here, in this problem Jack's date of birth was never mentioned to be the 14th, How is that assumed for our choice of answer to be correct because i could for any as long as the Sum of their ages give me anything between 1 and 31. Please help me understand.

1. 3,3,8

Lets break it down. The product of their ages is 72. So what are the possible choices?

2, 2, 18 sum(2, 2, 18) = 22
2, 4, 9 sum(2, 4, 9) = 15
2, 6, 6 sum(2, 6, 6) = 14
2, 3, 12 sum(2, 3, 12) = 17
3, 4, 6 sum(3, 4, 6) = 13
3, 3, 8 sum(3, 3, 8 ) = 14
1, 8, 9 sum(1,8,9) = 18
1, 3, 24 sum(1, 3, 24) = 28
1, 4, 18 sum(1, 4, 18) = 23
1, 2, 36 sum(1, 2, 36) = 39
1, 6, 12 sum(1, 6, 12) = 19

The sum of their ages is the same as your birth date. That could be anything from 1 to 31 but the fact that Jack was unable to find out the ages, it means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.

2, 6, 6 sum(2, 6, 6) = 14
3, 3, 8 sum(3, 3, 8 ) = 14

Since the eldest kid is taking piano lessons, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8.

1. Find out about Jack's birth date first.

Bill said that the sum of his kids ages is the same with Jack birth date. Jack still cannot make a guess because there were 2 combinations which are equals to his birth date. If all the numbers were different, Jack wouldn't have a problem to guess it at all. So, the only possible combination is (2,6,6) and (3,3,8) because both combinations have an equal sum. From this information, we can be sure that Jack's birth date is 14.

2. Bill's said that his eldest kid is just started taking piano lessons. So the (2,6,6) combination is automatically eliminated because Bill's doesn't have two eldest kids.

17. John is a jerk.

Why couldnt he just say my kids are 3, 3, 8?

Explanation:
Since, 72 is the product of the ages. So, possible combination of their ages can be :
1,2,36, sum=39
1,3,24, sum =28
1,6,12, sum=19
1,8,9, sum=18
2,2,18, sum=22
2,3,12, sum=17
2,4,9, sum=15
2,6,6, sum=14
3,3,8, sum=14
3,4,6, sum=13

Since, sum of their ages is same as Jack's Birth date, it can't be 1,2,36 as sum is more than 31.
Now,if Jack's date of birth is not 14,he would know the kids' ages, as all other combinations have unique some value.
Therefore,sum = Date of birth of Jack =14.
But, there are two combinations for it:
2,6,6 and 3,3,8
So, he was still not able to find the answer. When Bill told him that his eldest kid just started taking piano lessons, it means there is only one eldest kid.
so, 2,6,6 cant be the answer.

19. GREAT LOGIC PUZZLE! VERY CLEVER!!!!

20. logical""""""""""""""""""""""

21. silly question.

22. It's not that clever. "Two old friends meet after a long time"?? It turns out these two old friends happen to be a 14 year old boy and a man with 3 children...

1. Birthday means the day of the month, not the age in years !

23. One of the twins has to be the oldest - even if it's by 5 minutes. So still insufficient information given in the puzzle.

24. very nice one. enjoyed..

26. 24,3,1 as man biryjday concerned

27. The reason why it is 3,3,8 and not the other combinations is because Jack can do some incredible mental math computations in his head and found out that every combination of 3 ages that has a sum between 1 and 31 (or remembered his birthday, lol) and a product of 72 has a unique value except for 2 of those combinations: 3,3,8 and 2,6,6. He couldnt determine the conclusion given all of this information, and therefore needed to know that there was an oldest child before distinguishing between the 2 options.

If it were the other options he wouldnt have had to say he still didnt know, as those unique values would have made it clear.

28. ANSWER FOR THIS IS 3,3,8
3*3*8=72
3+3+8=14

BUT U GET PRODUCT WITH SO MANY COMBINATIONS AS SOMEONE ALREADY MENTIONED.
FROM ALL THOSE COMBINATIONS JACK CAN ELIMINATE ALL EXCEPT (3,3,8)& (6,6,2)
QUESTION..
HOW CAN HE ELIMINATE ALL OTHER COMBINATIONS..?
ANS:JACK IS AWARE OF HIS BIRTH DATE.
BUT JACK REPLIED THAT HE DOESN'T KNOW STILL..
THAT MEANS HE WAS CONFUSING TO SELECT ONE FROM THOSE TWO COMBINATIONS (3,3,8)& (6,6,2) WHOSE SUM IS 14 i.e. HIS BIRTH DATE.

NOW WE CAN ELIMINATE (6,6,2) BECAUSE BILL SAYS HIS ELDEST SON THAT MEANS HE HAS ONLY ONE ELDEST SON..NOT TWO ELDEST SONS

29. 6,8 and 9 years old

30. how u decide that that there are more than one combination result is only possible.why it cant be any other combination rather than result 14.bcoz bill told that he has three children.i cant get the answer properly

31. I think the answer should be 18, 4 and 1 respectively. This makes the eldest child 18 and capable of starting piano lessons. There is an eldest child so it stands correct to the description given. 18x4x1 = 72 and 18x4x1=23 which could by a birth date or an age for Jack. And the cherry on top, this means that there are no children of the same age which is genetically/mathematially improbable relative to the alternative theory of all kids being of different ages

32. You never mentioned a birthdate. Therefore any one of the answers with unequal numbers and a sum of 72 is a possibility. You messed up.

33. why cant be 1 9 8

34. 2, 4 and 9 ... I guest

35. Very good...

36. Whoa! That's a lot of comments!

37. Therefore JACK IS REALLY A MATH GENIUS, TO BE ABLE TO KNOW THE COMBINATION IN JUST A SHORT CONVERSATION^^

38. Answer is : 3 , 3, 8

it comes to two sets
2,6,6
3,3,8 which jack can't figure out.
but since Bill says he has a elder son so it should not be same ages
3, 3, 8

39. It's fun to see the explanations for all the wrong answers people gave here. Correct answer is without doubt 8,3,3 because that is the only case where sum of ages gives a number that has another combination and thats why jack couldnt figure out.

40. This comment has been removed by the author.

41. All we have gained from the conversation is that the product of their ages is 72 and the sum lies between (1,31) ; ie; (possible dates a month can have ).
So what are the possible choices?
2, 2, 18 sum(2, 2, 18) = 22
2, 4, 9 sum(2, 4, 9) = 15
2, 6, 6 sum(2, 6, 6) = 14
2, 3, 12 sum(2, 3, 12) = 17
3, 4, 6 sum(3, 4, 6) = 13
3, 3, 8 sum(3, 3, 8 ) = 14
1, 8, 9 sum(1,8,9) = 18
1, 3, 24 sum(1, 3, 24) = 28
1, 4, 18 sum(1, 4, 18) = 23
1, 2, 36 sum(1, 2, 36) = 39
1, 6, 12 sum(1, 6, 12) = 19
But we remember that Jack still had a problem figuring out their ages. It means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.
2, 6, 6 sum(2, 6, 6) = 14
3, 3, 8 sum(3, 3, 8 ) = 14
Now since the eldest kid is taking piano classes, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8.

42. The phrasing is flawed. It says, "the sum of their ages is the same as your BIRTH DATE." Merely saying "14" is not a date. However, saying "May 14" is a date.

The phrasing could potentially be improved this way:
"the sum of their ages is the same as the number of the day when you were born in May." Or something like that.