The hostess, at her 20th wedding anniversary party, tells you that her youngest child likes her to pose this problem to guests, and she proceeds to explain: "I normally ask guests to determine the ages of my three children, given the sum and products of their ages. Since Smith gave an incorrect answer to the problem tonight and Jones gave an incorrect answer at the party two years ago, I'll let you off the hook."

Your response is "No need to tell me more, their ages are..."

(In reply to solution 5 6 and 16 justification by Sachin)

{5,6,16} was my original answer also, but I don't think it's right now, because two years ago the ages would have been {3,4,14}, and if we make the assumption that no child under 3 would be posing brainteasers to adults at dinner parties, there would be no other set of ages with the same product and sum, where every age is 3 or above. {6,12,16} is the answer I favor.

Also, you were correct and I was wrong to think that the children's ages must be under 20, for fear of the "shotgun wedding". [The shotgun would have been late, anyway, if the children were 20 or above]. It is very common for a divorced or widowed woman to remarry and enter the second marriage with children from her previous marriage. It is so common that there is nothing "tricky" about assuming that it's possible. Maybe the nature of puzzles compels us to assume that the children were children of the marriage whose anniversay was being celebrated, but it is not explicitly stated in this puzzle. The woman could have married at 18, been widowed with three children at 25, remarried at 30, and then have been celebrating that 20th anniversay at the age of 50. Nothing unusual about that at all. But maybe in puzzles like this, that is considered "reaching". Who knows ?

I'll have to let this point gestate for a while, I guess.  

 

 

Posted by Penny on 2005-03-05 18:06:50