# Maths Riddle. **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [March 21, 2002, 7:46am UTC](https://boards.straightdope.com/t/maths-riddle/99312 "2002-03-21T07:46:38Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![100](https://avatars.discourse-cdn.com/v4/letter/1/a698b9/32.png) [@100](https://boards.straightdope.com/u/100)\ **Post date:** [March 21, 2002, 7:46am UTC](https://boards.straightdope.com/t/maths-riddle/99312/1 "2002-03-21T07:46:38Z")
My crazy Year 10 maths teacher gave us this riddle today here it is. Mr Smith and Mrs Jones are sitting down having a discussion about their families. Mrs Jones: How many children do you have? Mr Smith: I have 3 sons. Mrs Jones: How old are they? Mr Smith: I will give you a clue, when you multiply their ages, you get 36. Mrs Jones: That is not enough information! Mr Smith: Ok, here is another clue, when you add all 3 of their ages together, you get the number that is on my front door. _Mrs Jones gets up and looks at the number on the front door, comes back in and sits down.[_ Mrs Jones: That is STILL not enough information. Mr Smith: Your right. My Oldest son plays the trumpet. Mrs Jones: Ahhh, now i know! That was all the information we were given, word for word. I have the answer to this riddle, but i wanna see if it is solved by anyone else. You can ask any questions, but DONT ASK FOR THE ANSWER! 😃 First correct answer wins! ---
**Author:** ![ricecake](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@ricecake](https://boards.straightdope.com/u/ricecake)\ **Post date:** [March 21, 2002, 7:59am UTC](https://boards.straightdope.com/t/maths-riddle/99312/2 "2002-03-21T07:59:55Z")
im going to refrain from flaming ---
**Author:** ![100](https://avatars.discourse-cdn.com/v4/letter/1/a698b9/32.png) [@100](https://boards.straightdope.com/u/100)\ **Post date:** [March 21, 2002, 8:10am UTC](https://boards.straightdope.com/t/maths-riddle/99312/3 "2002-03-21T08:10:54Z")
Huh? Is this the wrong forum? Sorry, i will have a mod take care of this a.s.a.p ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [March 21, 2002, 8:11am UTC](https://boards.straightdope.com/t/maths-riddle/99312/4 "2002-03-21T08:11:34Z")
It’s a good riddle (defined as one I can solve). But it doesn’t really belong in GQ, which is for questions you don’t already know the answer to. I’ll move it to MPSIMS. ---
**Author:** ![Stimpson](https://avatars.discourse-cdn.com/v4/letter/s/46a35a/32.png) [@Stimpson](https://boards.straightdope.com/u/Stimpson)\ **Post date:** [March 21, 2002, 8:23am UTC](https://boards.straightdope.com/t/maths-riddle/99312/5 "2002-03-21T08:23:11Z")
The suspense is killing me! The boys are 2, 2, and 9. Combinations of three numbers whose product is 36 {I hope I got them all…}: 1, 1, 36 1, 2, 18 1, 3, 12 1, 4, 9 1, 6, 6 2, 2, 9 2, 3, 6 3, 3, 4 So that’s not enough information. So Mrs. Jones checks out the front door, but that’s still not enough information. The “address” must be 13, because only two combinations have the same sum (1,6,6 and 2,2,9). Then Mr. Smith makes a costly error: he divulges that he has an eldest son. In the 1,6,6 combination, we ~assume~ the six year olds are the same age; that is, there is no eldest son. Therefore, the boys must be 2, 2, and 9. Mindless? Perhaps. Pointless? Probably. My question is how old is your crazy math teacher, because methinks this is an old riddle. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [March 21, 2002, 8:44am UTC](https://boards.straightdope.com/t/maths-riddle/99312/6 "2002-03-21T08:44:42Z")
> [@](#): > > \*Originally posted by 100% \* > My crazy Year 10 maths teacher gave us this riddle today here it is. So you want some deductions, huh\*? Your use of the word ‘crazy’ and missing punctuation between ‘today’ and ‘here’ suggests to me that you are a young person. > [@](#): > > \*Originally posted by 100% \* > I have the answer to this riddle, but i wanna see if it is solved by anyone else. > You can ask any questions, but DONT ASK FOR THE ANSWER! > > First correct answer wins! My previous assessment concerning your age is confirmed by your use of ‘wanna’. Also, why would I want to ask questions? (except ‘what does the first correct answer win?’) As for the puzzle (it’s not a riddle), I have my suspicions about the trumpet, but here goes. 1. A woman has 3 sons, whose ages multiply to 36. I’ll assume their ages are expressed as integers. Later the sum of their ages will be important, so I’ll put that in as well. Possible combinations are (including twins): 1 1 36 = 38 1 2 18 = 21 1 3 12 = 16 1 4 9 = 14 1 6 6 = 13 2 3 6 = 11 2 2 9 = 13 3 3 4 = 10 Since knowing the total of their ages is insufficient, there must be two equal totals. These would be 1 6 6 and 2 2 9. (So Mrs. Jones could have remarked that Mrs. Smith had twins.) Instead we learn that ‘the oldest son plays the trumpet’. Well I’ve never heard of two babies emerging simultaneously (though if it has happened, this board will undoubtedly know about it!), so even twins boys yield an ‘oldest son’. So presumably the answer relies on the fact that nobody plays the trumpet at age 6. From the website of the ‘Walnut Grove School of Music & Guildford School of Music’: Trumpet The trumpet requires physical exertion and lung power. 9 years and older is a good time to start the trumpet. So the answer is 2,2 and 9 years old. \*an attempt to speak teenager… ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [March 21, 2002, 6:02pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/7 "2002-03-21T18:02:18Z")
Fraternal twins could be a boy and a girl, so you can’t rule out 6-year-old twins. And maybe the boy happens to be a child prodigy, playing the trumpet already. Tell your teacher his or her puzzle is flawed. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [March 21, 2002, 6:03pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/8 "2002-03-21T18:03:37Z")
> [@](#): > > Mr Smith: I have 3 sons. Doh! :rolleyes: ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [March 21, 2002, 7:37pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/9 "2002-03-21T19:37:23Z")
> [@](#): > > \*Originally posted by glee \* > Well I’ve never heard of two babies emerging simultaneously (though if it has happened, this board will undoubtedly know about it!), so even twins boys yield an ‘oldest son’. > So presumably the answer relies on the fact that nobody plays the trumpet at age 6. > > From the website of the ‘Walnut Grove School of Music > & Guildford School of Music’: > > Trumpet > The trumpet requires physical exertion and lung power. 9 years and older is a good time to start the trumpet. > > So the answer is 2,2 and 9 years old. glee, I take my hat off to you. I always thought that the reasoning “there is no oldest if ages are 6 and 6” was bogus. However you have provided convincing evidence that the correct answer should be 2, 2 and 9. At first I thought you were kidding with your cite but I [looked it up](http://www.optionz.com/education/music/) and it was indeed accurate. (still in awe at the magnificent answer) ---
**Author:** ![Neptune](https://avatars.discourse-cdn.com/v4/letter/n/b5a626/32.png) [@Neptune](https://boards.straightdope.com/u/Neptune)\ **Post date:** [March 21, 2002, 8:06pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/10 "2002-03-21T20:06:59Z")
Two six year old brothers need not be twins. One could be, say, six years and one day, and the other six years and three-hundred-sixty days, if I understand the human gestation process. Also, since the speaker is _Mister_ Smith, he could have sons by different women that differ in age by any interval. I like the “lung power” argument, though. That’s a new twist on the problem that I’ve never heard before. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [March 21, 2002, 8:18pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/11 "2002-03-21T20:18:15Z")
> [@](#): > > \*Originally posted by Neptune \* > Also, since the speaker is _Mister_ Smith, he could have sons by different women that differ in age by any interval. Neptune, you dirty dog! Is there something about you you’re not telling us? :eek: ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [March 22, 2002, 1:01am UTC](https://boards.straightdope.com/t/maths-riddle/99312/12 "2002-03-22T01:01:44Z")
okay, given that children of the same age would be out, and given that to play the trumpet one must be 9, what eliminates these combinations… 1, 1, 36 1, 2, 18 1, 3, 12 1, 4, 9 ??? why are these not valid? am i missing something? ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [March 22, 2002, 1:05am UTC](https://boards.straightdope.com/t/maths-riddle/99312/13 "2002-03-22T01:05:29Z")
Ludovic - you have to assume that Mrs. Jones knows what she’s doing. If the ages were 1, 1, 36, then the house number would be 38. Mrs. Jones, upon seeing the house number 38, would know “there is only one set of numbers that would work, so I have sufficient information to determine the answer.” Since upon seeing the house number she says “there’s not enough information”, that means that there are more than one set of ages that could add up to the house number. ---
**Author:** ![Stimpson](https://avatars.discourse-cdn.com/v4/letter/s/46a35a/32.png) [@Stimpson](https://boards.straightdope.com/u/Stimpson)\ **Post date:** [March 22, 2002, 9:33pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/14 "2002-03-22T21:33:05Z")
Not to defecate on anyone’s shindig, but I think you guys are reading into the ‘My oldest son plays the trumpet’ clue a little bit too much. The important word in the clue is “oldest,” not “trumpet.” The predicate is meant to be arbitrary; to cause people who use “your” instead of “you’re” to ask themselves “what does that have to do with the problem?” Unfortunately, what was meant to be arbitrary has been deemed essential. While I appreciate **glee** ’s enthusiasm and creativity, they are better directed toward more fruitful pursuits than “crazy Year 10 maths” puzzles. Also, **glee** and I assumed {correctly} that the ages were to be expressed as integers. Otherwise, things get messy-- I see **Neptune** has considered the possibility of large values of six :D. But note that if the ages are 1, 6 and 1/365th, and 6 and 360/365ths, the product is no longer 36. More considerations: - The number on Mr. Smith’s door is irrational, imaginary, mixed… - “The trumpet” is a role in the school play, perfectly suitable for a six-year-old. - Why is Mr. Smith being such a hardass about saying how old his kids are? ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [March 23, 2002, 12:55pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/15 "2002-03-23T12:55:58Z")
> [@](#): > > \*Originally posted by Stimpson \* > Not to defecate on anyone’s shindig, but I think you guys are reading into the ‘My oldest son plays the trumpet’ clue a little bit too much. The important word in the clue is “oldest,” not “trumpet.” The predicate is meant to be arbitrary; to cause people who use “your” instead of “you’re” to ask themselves “what does that have to do with the problem?” Unfortunately, what was meant to be arbitrary has been deemed essential. While I appreciate **glee** ’s enthusiasm and creativity, they are better directed toward more fruitful pursuits than “crazy Year 10 maths” puzzles. I thought I’d dealt with the ‘oldest’ bit. I’ve taught identical twins where, **as they told me** , one was the **oldest** by 20 minutes. Are you saying this is not correct use of English?! If a puzzle said ‘X has a child’, and X’s possible ages were 2 and 22, are you going to suggest it’s **equally likely** that a 22 year old has a child, or that cells were extracted from a 2 year old and used in some genetic cloning procedure?! > [@](#): > > \*Originally posted by Stimpson \* > More considerations: > > - The number on Mr. Smith’s door is irrational, imaginary, mixed… > - “The trumpet” is a role in the school play, perfectly suitable for a six-year-old. Cite please, for the % of doors, with numbers on, that are ‘irrational, imaginary, mixed’ 😕 Yes the kid could be playing a role entitled ‘The trumpet’. I myself was the baby Jesus once, in a Nativity play. (depressingly my performance was not highly-rated). But again you are invited to research the likelihood of this, compared to the phrase ‘my son plays the trumpet’ being a musical reference. Also it is surely not a coincidence that the first website I looked at gave 9 as the age. Stimpson, you’re just sore because I got it right! Now that nice Mr. Winkelried knows how to acknowledge a decent posting. He, Sir, is a **true gentleman**. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [March 23, 2002, 1:04pm UTC](https://boards.straightdope.com/t/maths-riddle/99312/16 "2002-03-23T13:04:30Z")
well I don’t care! (Thanks again, Arnold 🆒 )