

Subject:
Obscure Mathematical Riddle
Category: Science > Math Asked by: isarpsdga List Price: $20.00 
Posted:
17 Jan 2005 20:41 PST
Expires: 16 Feb 2005 20:41 PST Question ID: 459025 
On October 28, 2002, a mathematical riddle was posted on a newsgroup for a University of Illinois (UrbanaChampaign) Computer Science course. The only information I have as to the origin of the riddle is the title of the thread, "Interesting Problem from Iowa State." The newsgroup server has since been shut down, so I cannot access the original post or any followup replies. I still have not figured out the answer to this riddle, over two years later. Here's the riddle:  Three mathematicians are talking. "How many kids do you have?" The first asks the second mathematician. "Three," she answers. "How old are they?" he asks. "Well if you multiply their ages, you get 72. But if you add them, you get your office number." She says. The first mathematician thinks for a few seconds and says, "I do not think there is enough information for me to solve this!" he says. The mother mathematician immediately says, "Oh, of course, I forgot to tell you that the eldest plays the violin!"  Please end my torment, and find for me: 1) The ages of the children. 2) The office number of the first mathematician. I already attempted the shotgun approach of simply saying "any combination of ages such that their product is 72 and one is bigger than the others; it's 'probably' 2, 4, 9, or maybe 3, 4, 6," and that was shot down. There is supposedly one pair of answers, and that's what I'm looking for. 

Subject:
Re: Obscure Mathematical Riddle
Answered By: pinkfreudga on 17 Jan 2005 21:05 PST Rated: 
The children's ages (including a pair of twins!) are 3, 3, and 8. The office number is 14. Substantially the same puzzle, with superficial changes, is posted on a University of Calgary site: "A census taker comes to a man's home. Upon inquiring about the ages of his three children, he receives the following reply. 'If you multiply their ages, you get 72. Furthermore, the sum of their ages is the house number' (which the census taker knows). The census taker considers the situation for a moment, then says, 'Okay. I need one more piece of information.' 'Sure thing,' replies the man. 'My oldest child loves chocolate.' The census taker smiles, thanks the man, and walks away. How old are the man's three children? Answer: factor 72 to 1*2*2*2*3*3 123: 1,2*2,2*3*3 = 1+4+18 = 23 1,2*3,2*2*3 = 1+6+12 = 19 1,3*3,2*2*2 = 1+9+8 = 18 114: 1,2,2*2*3*3 = 1+2+36 = 39 1,3,2*2*2*3 = 1+3+24 = 28 115: 1,1,2*2*2*3*3 = 1+1+72 = 74 113: 2,2,2*3*3 = 2+2+18 = 22 2,3,2*2*3 = 2+3+12 = 17 3,3,2*2*2 = 3+3+8 = 14 122: 2,2*2,3*3 = 2+4+9 = 15 2,2*3,2*3 = 2+6+6 = 14 3,2*2,2*3 = 3+4+6 = 13 We don't have to know the house number. The fact that the census taker knows the house number and that's not enough for him to determine the childrens' ages tells us that it must be ambiguous. There is only one sum that comes up more than once, it's 14. Therefore, that must be the one. Because there *is* an oldest child, their ages are 3,3,8." University of Calgary: A Collection of Riddles and Puzzles For DMs http://www.ucalgary.ca/~ammaster/d_n_d/puzzles.html Here you'll find another version, also mathematically identical to your puzzle, with some students' solutions: Math Forum: Strawberry Ice Cream, April 2024, 1998 http://mathforum.org/elempow/fullsolutions/19980420.fullsolution.html And yet another: Winchester Public Schools: Answer to November 9, 1998 Problem http://www.pen.k12.va.us/Div/Winchester/jhhs/math/probweek/a110998.html My Google search strategy: Google Web Search: "if you multiply their ages, you get 72" ://www.google.com/search?hl=en&q=%22if+you+multiply+their+ages%2C+you+get+72 I hope this is precisely what you need. If it is not, please request clarification; I'll gladly offer further assistance before you rate my answer. Best regards, pinkfreud 
isarpsdga
rated this answer:
and gave an additional tip of:
$2.00
Hah! Such a ridiculously simple answer, and after all this time I still never figured it out. This is why I didn't do too well on my theoretical CS courses. ;) Exactly what I was looking for. Thanks for the prompt response  I may now rest easy at night. 

Subject:
Re: Obscure Mathematical Riddle
From: pinkfreudga on 18 Jan 2005 10:20 PST 
Thank you for the five stars and the nice tip! ~pinkfreud 
Subject:
Re: Obscure Mathematical Riddle
From: samuelbga on 18 Jan 2005 10:24 PST 
I'm more puzzled now. Please forgive me if I'm slow or naive but, can anyone tell me how the fact that a child plays violin or likes chocolat is relevant to solve the riddle? 
Subject:
Re: Obscure Mathematical Riddle
From: pinkfreudga on 18 Jan 2005 10:54 PST 
samuelb, The remark about the oldest child playing violin or liking chocolate is relevant only because it establishes that there is one "oldest" child. This eliminates the 2, 6 and 6 possibility. 
Subject:
Re: Obscure Mathematical Riddle
From: dljones913ga on 18 Jan 2005 13:50 PST 
Maybe, I am just dumb but why can't the ages be: 9 8 1 9*8*1 = 72 Just wondering? 
Subject:
Re: Obscure Mathematical Riddle
From: pinkfreudga on 18 Jan 2005 14:13 PST 
djones913, The ages must add up to 14, since that is the only ambiguous possibility that would require the additional info about the eldest child. If the children were 9, 8, and 1, the mathematician (knowing his own office number  in this case, 18) would not have required the hint about one child being the eldest, and would have been able to give an answer immediately upon learning that the product of the ages was 72 and the sum of the ages was the same as his office number. 
Subject:
Re: Obscure Mathematical Riddle
From: samuelbga on 18 Jan 2005 15:44 PST 
Dear Pink, Got it. Thanks! 
Subject:
Re: Obscure Mathematical Riddle
From: stapalheadga on 19 Jan 2005 11:14 PST 
This reminded me of a somewhat similar, albeit much more complicated, puzzle that can be found at http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=puzzle086. It's very interesting. 
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