SAM and john were thick friends in childhood. But as part of studies, SAM went to america and JOHN to london.

After several years sam went to london for his higher studies. He accidently came to meet his old friend. JOHN said he was now married and has three children. When SAM asked their ages, the john said that the product of their ages is 36. sam asked for another clue and the john asked if he could see the number on the house across the street. When sam said yes, john said that the sum of their ages equaled that number. sam said he still could not determine their ages. Then john said that his oldest child has red hair. Finally sam knew their ages. What were their ages and how did he know?

• given that there are 3 children
  
  the product of their ages =36
  
  a x b x c=36
  
  now let's check the product combinations of 36
  
  9 x 4 x 1
  9 x 2 x 2
  6 x 6 x 1
  6 x 3 x 2
  12 x 3 x 1
  18 x 2 x 1
  4 x 3 x 3 totally 7 combinations
  
  also given that the sum of their ages =house number
  but house number is not given
  
  so checking combinations we have
  
  a + b + c= house number
  
  9+4+1=14
  9+2+2=13
  6+6+1=13
  6+3+2=11
  12+3+1=16
  18+2+1=21
  4+3+3=10
  
  also given that sam couldnot find the values even after knowing the house number
  
  this indicates that he might have come across a problem of getting two ormore combinations of their ages equalling the house number
  
  now if we check the cases
  we have
  two combinations (9,2,2) and (6,6,1) having a count of 13
  
  also given that the oldest child has red hair
  which means that there is only one child who is elder than the rest
  
  so the problem comes to an end
  
  the combination of (9,2,2) justifies both the situations
  
  HENCE the ages of the children are 9 ,2 ,2 respectively
• 12 years agoHelpfull: Yes(3) No(1)
• 9,2,2
  36=1*6*6
  =1*2*18
  =1*3*12,.....consider all combinations
  
  sum of their ages is house number.but then also he can´t answer.that means there are two or more combinations in which sums are equal
  
  like 1,6,6 and 2,2,9
  
  oldest has red hair .therefore answer is 2,2,9
• 12 years agoHelpfull: Yes(1) No(1)