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..."

I get a different answer than Charlie, so mine must be wrong.

The ages are 5, 6 and 16.

I assumed that since the woman was married 20 years ago, the children can be no more than 19 years old. (It wasn't a shotgun wedding). Also, "the youngest" implies that the smallest age is unique. Finally, since "the youngest" was posing the problem two years ago, he/she must have been as least 1 then, and at least 3 now. (1 may not be too young to pose a relatively simple question about ages. I've seen some very articulate 1-year-olds). 

The ages {5,6,16} have product=480 and sum=27, as do the ages {4,8,15}, which is why Smith was able to guess wrong tonight.

Two years ago the ages were {3,4,14}. These ages have product=168 and sum=21, as also do the ages {2,7,12}, which is why Jones was able to guess wrong two years ago.

{5,6,16} are the only ages my program found in the 3-19 range such that they have nonunique product and sum now and had nonunique product and sum 2 years ago also.

 

 

Edited on March 4, 2005, 12:57 am

Posted by Penny on 2005-03-04 00:33:45