Conversation between two mathematicians:

First: I have three children. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbor's door number on my left. The second mathematician verifies the door number and says that it is not sufficient. Then the first says "Ok one more clue is that my youngest is really the youngest". Immediately the second mathematician answers. Can you answer the question asked by the first mathematician? What are the children ages?

• Possible options for same sum of ages ( 13 here)with product of ages as 36 are
  2,2,9
  and
  6,6,1
  
  but in case of 2,2,9
  youngest is not really youngest as two children of age 2 years are twins.
  whereas
  in case of 6,6,1
  youngest is really youngest.
  
  so 6,6, 1 is correct.
• 12 years agoHelpfull: Yes(3) No(3)
• It have following four possibilities which satisfies all the conditions.
  
  Ages will be = 1,6,6 (product = 36 ; sum = 13)
  1,3,12 (product = 36 ; sum = 16)
  1,4,9 (product = 36; sum = 14) and
  2,3,6 (product = 36; sum = 11).
• 12 years agoHelpfull: Yes(2) No(4)