perplexus.info :: Logic : How old did you say they were?

How old did you say they were? (Posted on 2005-03-03)

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..."

Submitted by Erik O.

Rating: 3.2000 (10 votes)

Solution: (Hide)

We must find cases where (1) the oldest child is less than 20, (2) the two younger children have different ages, AND (3) there is a sum and product that give rise to some ambiguity for the ages both this year and two years ago.
There is only one set of ages that accomplishes all three conditions: (5, 6, 16).
The same product and sum could be achieved by (4, 8, 15), which must have been guessed by Smith, and the product and sum two years ago could have been (2, 7, 12), which must be what Jones guessed two years ago.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Ages	Math Man	2011-07-07 15:50:25
Answer	K Sengupta	2008-10-25 01:04:11
no program, no solution?	Terence	2005-11-11 11:11:21
Is this correct?	Brandon	2005-05-21 15:27:20
a logical solution	abo3abed	2005-03-22 05:39:03
statement	gary wallravin	2005-03-20 23:14:00
re(2): A lot of assumptions.	john	2005-03-14 14:31:49
I think the answer is	louis	2005-03-10 17:12:53
is the answer	louis	2005-03-10 17:05:49
re: A lot of assumptions.	Dustin	2005-03-09 17:43:26
A lot of assumptions.	john	2005-03-09 17:18:08
My Guess	Warren	2005-03-08 07:12:37
re(4): On second thought.....	Penny	2005-03-06 14:40:45
re(3): On second thought.....	Sachin	2005-03-05 20:49:20
re(2): On second thought.....	Charlie	2005-03-05 20:20:12
re: On second thought.....	Sachin	2005-03-05 19:14:58
On second thought.....	Penny	2005-03-05 18:20:36
re: solution 5 6 and 16 justification	Penny	2005-03-05 18:06:50
sorry for giving sol in subject	Sachin	2005-03-05 17:31:00
solution 5 6 and 16 justification	Sachin	2005-03-05 17:02:29
solution 5 6 and 16 (C++ program)	Sachin	2005-03-05 16:30:34
solutaion 5 6 and 16	Sachin	2005-03-05 16:27:23
re(5): Solution (??)	Penny	2005-03-05 03:25:06
re(4): Solution (??)	Charlie	2005-03-04 18:47:53
re(3): Solution (??)	Charlie	2005-03-04 18:17:49
re(2): Solution (??)	Penny	2005-03-04 17:20:23
Solution	clyde	2005-03-04 15:29:38
My guess (??)	Les	2005-03-04 15:28:02
re: Solution (??)	Charlie	2005-03-04 13:59:36
Solution (??)	Penny	2005-03-04 00:33:45
solution	Charlie	2005-03-03 20:47:33

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