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?

• Product of the 3 ages must be 72.
  The sum of their ages is also known.Still Jack is not able to calculate the ages of the 3 kids.This implies more than one case gives product 72 and sum the same value.
  ie the values are
  ===> (2,6,6) and (3,3,8)
  Both their product = 72 and sum = 14
  
  Given the eldest kid just started taking piano lessons.
  So they are 3,3 and 8 years old.(there should be an eldest kid. so 2,6,6 is not their age)
  
  
• 10 years agoHelpfull: Yes(10) No(1)
• 3,3 and 8 years old
  
• 10 years agoHelpfull: Yes(2) No(1)
• @Saraswathy
  We dont know his birth date but he knows.
  
  Let us say x,y, and z are their ages and sum of their age s
  x*y*z = 72
  x+y+z = s
  
  If we take x = 2, y=4 and z = 9
  s = 2+4+9 = 15
  For no other values of x, y and z the sum is 15(product must always be 72)
  So if Jack's birth date is 15, he would be sure that the ages of Bill's kids are 2,4 and 9.But He still couldn't calculate the ages of kids.So his birth date is not 15.
  
• 10 years agoHelpfull: Yes(2) No(2)
• the product of the ages are 72
  so, the three ages are factors of 72
  piano classes start at above 5 years children
  so, we start from 5
  5 is not a factor of 72
  so, we go for 6
  after divide 72 with 6, remaining 12
  eldest kid age-6
  remaning two kids age-3 &4
  so, kids ages are:3,4&6
• 10 years agoHelpfull: Yes(2) No(1)
• (2,4,9) is also possible...
  
  We cannot determine as we don't know Jack's birth date...
• 10 years agoHelpfull: Yes(1) No(0)
• Thank you @Ann... Now am getting...
• 10 years agoHelpfull: Yes(1) No(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.it is right
  
• 10 years agoHelpfull: Yes(1) No(1)
• ms theresa can u explain ur answer?
  
• 10 years agoHelpfull: Yes(0) No(0)
• @ann theressa thanks yar, for solution
  
• 10 years agoHelpfull: Yes(0) No(0)
• 3,3,8 is the answer
• 10 years agoHelpfull: Yes(0) No(0)
• 2,3,12 is also possible
  
• 10 years agoHelpfull: Yes(0) No(0)
• 3,3,8
  since
  the instances of 72 are........
  we can get it frpm final clue
  
• 10 years agoHelpfull: Yes(0) No(0)
• dkcmdkmcdkmcdkmcs
• 8 years agoHelpfull: Yes(0) No(0)