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# My Teachers Three Kids: Newsletter Challenge (06/05/07)

Posted June 03, 2007 5:01 PM
Pathfinder Tags: challenge questions

The question as it appears in the 06/05 edition of Specs & Techs from GlobalSpec:

Tom meets his old math teacher John.
"Hello John, how old are your three children now?"
"Well, if you multiply their ages together you get 36, and, if you add their ages you get the number on that bus."
Tom is perplexed, so after a while John adds, "Oh! And the oldest plays the piano," at which point Tom is happy.

How old are the three children? What number is on the bus?

Thanks to Randall who submitted the original question.

(Update: June 12, 8:39 AM EST) And the Answer is...

The trick is in realising that the first two bits of information are not quite enough for Tom to arrive at a unique solution. The final snippet (somewhat obliquely) resolves his dilemma.

There are only eight possible combinations of ages which when multiplied together give 36.

1, 1, 36 (sum 38)
1, 2, 18 (sum 21)
1, 3, 12 (sum 16)
1, 4, 9 (sum 14)
1, 6, 6 (sum 13)
2, 2, 9 (sum 13)
2, 3, 6 (sum 11)
3, 3, 4 (sum 10)

If the number on the bus had been anything other than 13 then Tom would have known immediately how old all the children were. Of the two possibilities which add up to 13 only the answer [2, 2, 9] has an "oldest" child, and, this is therefore the answer.

Congrats to ve9gfi for beign the first to correctly answer the puzzle.

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Anonymous Poster
#74

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/05/2007 9:50 PM

Ages 1, 2 & 18 = #21 Bus

Ages 1, 3 & 12 = #16 Bus;

Ages 1, 4 & 9 = #14 Bus;

Ages 2, 3 & 6 = #11 Bus

And with twins:

Ages 1, 6 & 6 = #13 Bus (one twin will be slightly older than the other);

Ages 3, 3 & 4 = #10 Bus;

Ages 2, 2 & 9 = #13 Bus; and

Pity the wife--Ages 1, 1 & 36 = #38 Bus

Anonymous Poster
#75

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/05/2007 10:14 PM

ages 6-3-2 Bus number 11

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#76

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 12:49 AM

Eldest child is 4 years & twins of 3 years age. The number on that bus is 10.

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#86

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 6:43 AM

A cat would be able to play better. (three blind mice - the clock struck one the other two got away)

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#78

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 1:50 AM

Answer is 2+2+9, bus 13. It was not difficult.

RF

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#79

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 2:02 AM

Never is when you copy.

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#80

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 4:10 AM

I make it 2, 2, 9 and bus number 13. Other combinations give unique sum, so Tom would have been able to work it out at that point. 2, 2, 9 and 1, 6, 6 both add to 13 but 1, 6, 6 doesn't have an oldest.

I haven't looked at other postings yet, I'll do that now.

Cheers.....Codey

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#83

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 5:37 AM

"1, 6, 6" doesn't have an oldest. 6 and 6 can have as much as 364 days between them. Even twins don't drop simultaneously. Surely not even a maths teacher would be that sloppy in his use of English?

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#84

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 6:03 AM

Hi Guest - but we're talking about nominal ages here i.e. whole number of years before last birthday. #11 and one or two others used same logic. I'm pretty confident "official" answer will be what we've said.

Codey

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#85

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 6:22 AM

I agree - Randall must be slipping...

Anonymous Poster
#89

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 7:13 AM

....oh no Randall . They didn't even add that "..which we modified a bit " qualifier..

Quick , hide.

Anonymous Poster
#93

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 7:49 AM

The question implies that Tom sees the bus number and is puzzled until he learns that there is an oldest child. Since the product of the ages always equals 36, I infer that the sums of two or more possible answers are the same, i.e., the bus number. Trying all possible permutations yields 1, 6, and 6 or 2, 2, and 9 as the only answers which give the same sum. Since 2, 2, and 9 has an oldest child, that is the answer and the bus is indeed lucky 13.

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#96

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 8:50 AM

Well look tha ealder child has 9

and other's are 4,1 aged

Bus number:14

Anonymous Poster
#98

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 9:00 AM

3,3,4. Bus is 10

Anonymous Poster
#100

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 9:17 AM

Especially: "an easier number puzzle..."

Point taken, I hope

Anonymous Poster
#101

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 9:44 AM

my guess is 9,2,2 - multplies to 36 and adds to 13, Tom was perplexed when he saw the bus was number 13, because the ages 1,6,6 would have also added to 13 (these were the only combinations that had the same sum). Once he knew the oldest played piano (vs. twins which would not be "oldest") he had the answer.

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#103

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 1:10 PM

<sulk>

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#104

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 1:21 PM

Hmm...kris the horn persona seems to bring the moody side of you... And I liked the squirrel better...

Bring him back...bring him baaacchkkk....Just playing with you

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#105

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 1:34 PM

Have no fear , the furry one is beside me. Paradoxically , I am 'beside myself' as I said something a bit too on topic (which in itself , is bizarre for me) and got edited.

<fake sulk>

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#106

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 1:43 PM

Which leaves the replies to that input rather incomprehensible

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#107

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 2:18 PM

Indeed it does !

<annoyance on>

A: Not many in this case + irrelevant - the fun types will take a hint with "<spoiler>" and enjoy the game by not looking , the dishonest will pretend not to have read but post an 'original' solution anyway.

Recent questions lend themselves to this quite 'admirably'.

Edit control clearly thinks there is more time for this to run. Odd , when overt spoiler reference to Monty Hall were allowed to pass.

<annoyance off>

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#108

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/06/2007 3:59 PM

As a perfectly well presented version of the official solution was posed so early by ge9vfi, I wonder why they bothered.

BTW, I think I finally have the definitive solution:
-2+1.414i , -2-1.414i , 6 bus #2
The alternative that the oldest+piano clue eliminated was
-1+2.828i , -1-2.828i , 4 (also bus #2, of course)

Tortured reasoning:
Clearly, John consistently treats questions in this manner. Therefore, he will by now have driven his wife insane. This will have had disastrous consequences for the younger children, who will be negative, have all sorts of complexes, and otherwise be irrational. As an obvious mathematical pedant, he will not have made the mistake of using "oldest" where "greatest age" would be correct - so it's the piano that is the clue. And it would be rather unusual for two people to think they knew that six is too young to play the piano (four is not necessarily too young, but is more commonly believed to be).

Other eliminated option: bus #4 - that has three solutions that satisfy the reasoning, but two of them have the same oldest age of 8.

Fyz

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#110

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 3:31 AM

If Tom already knew that John had three children, it is likely that he would have known that one was older.

In any conversation about children, when the number of offspring is mentioned, the next question asks about ages/sexes.

(5kids= plenty experience)

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#111

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 5:13 AM

Henry Allingham has just turned 110 , and I think I heard his eldest was 87. Respect ! What a great character.<applause>

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#112

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 6:22 AM

<applause>

My great-grandfather fought in HMS Lion at the Battle of Jutland (and survived that).

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Anonymous Poster
#114

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 10:54 AM

The age of the three children are 9,2 and 2. The number on the bus is 13.

Anonymous Poster
#115

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 2:22 PM

In a "normal" sense the children must be 9,4 & 1 year old.

Can be others ages but "untypical" if you let me.

So bus number is 9+4+1=14.

Bye

Anonymous Poster
#116

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 3:50 PM

I think Tom is a musician and he knows the oldest child is his !

Anonymous Poster
#117

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/07/2007 4:52 PM

This is a total calumny. Tom would have been twelve at the time, and I his house-mistress. Publish an apology, or CR4 will be hearing from my lawyers.

Jean Yong de-Fleur

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#118

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/08/2007 1:50 AM

Isn't it more likely the youngest is Toms ?

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#119

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/08/2007 4:27 AM

Yes, but that is number 4 for John's wife - hence only asking about "your three kids".

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#120

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/08/2007 6:34 AM

I was thinking John was busy marking papers while Tom got busy helping his wife concieve child 3 in the stock-room. Naughty Tom , John never noticed though.

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#121

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/08/2007 6:43 AM

Both the younger children are 2 years old. Unlikely that she'd be that keen on a new liaison so soon after producing number 2 - so, either both 2 & 3 (twins), or neither.

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#122

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/08/2007 7:00 AM
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#123

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/08/2007 7:16 AM

That's true, albeit relatively uncommon - but still question as to why so certain number 3 rather than number 2

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#124

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/09/2007 4:15 PM

Let's look at the social clues here...

Tom and John are on a first name basis. This is uncommon between teachers and students, but more likely to happen if the teacher is young when he or she first meets the student. John is named as Tom's teacher, not his professor, so they first met before Tom went to college. I believe Tom is in high school at the time of the current encounter, I'll explain in a moment.

Tom knows John has three children. How does he know this? Because John spoke about them in class, but some time has passed, or Tom would not be asking about their ages.

They are standing near a bus, so they are most likely on a school campus. That's one reason why I think Tom is still in high school.

John says "the oldest plays the piano." This implies that the child has taken lessons, prcaticed regularly, and has had time to develop his or her talent. This favors the oldest being 12. If the child were much older, Tom would most likely have been aware of that without John mentioning that fact.

The encounter in question takes place on the first day of a new school year. Tom was in John's class last year. John spoke about his 3 children, especially his then newborn baby. He also talks a lot about having to pay for piano lessons, which the ch8ild has now completed. Tom and John meet on their way into the school, or just inside the entrance. Because Tom is not in any of John's classes this year, he regards Tom as his "old" teacher, despite his age.

The children are 1, 3, and 12, the bus numer is 16.

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#125

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/09/2007 4:48 PM

I notice the correct answer above but it is not motivated properly.

At first Tom had only the 36 and the bus number,

To be perplexed tom must have had at least 2 matching possibilities

These possibilities are

1,6,6 = 13

2,2,9 = 13

With the added clue of the oldest playing the piano Tom was able to calculate the ages.

And he chose 2,2,9

Motivation

A child of 9 has a better change of playing the piano but it cannot be considered conclusive because.

• 6 year olds may also play and
• One of twins is always called the oldest.

It is therefore possible that the oldest of the 2 could have shown talent and receive lessons and indeed play the piano.

More clues must therefore be considered

This clue was that he is a math teacher.

A math teacher is trained to partially ignore errors (math , copy or other) when scoring exams or tests.

He must continue marking the answer in spite of an error (for method and knowledge).

He would therefore not discard the potential of one of his children just because he or she did not show a talent right away.

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#126

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/09/2007 4:59 PM

The correct answer is /are given above but it is not motivated.

At first Tom had only the 36 and the bus number,

To be perplexed tom must have had at least 2 matching possibilities

These possibilities are

1,6,6 = 13

2,2,9 = 13

With the added clue of the oldest playing the piano Tom was able to calculate the ages.

And he chose 2,2,9

Motivation

A child of 9 has a better change of playing the piano but it cannot be considered conclusive because.

• 6 year olds may also play and
• One of twins is always called the oldest
• If the oldest showed talent (the younger did not) he would have been enrolled for lessons and could play.

More clues must therefore be considered

And the clue is that John is a math teacher

A math teacher is trained to partially ignore errors (math , copy or other) when scoring exams or tests.

He must continue marking the answer in spite of an error (for method and knowledge).

He would therefore not discard the potential of one of his children just because he or she did not show a talent right away.

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#128

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/11/2007 5:28 AM

Regardless of talent, I doubt if a 2, 4 or 6 year old would have hands big enough to operate a piano keyboard - but that is my ignorance speaking.

My logic was posted in #62. But I got it wrong because by bad luck I missed out 2,2 & 9 = 13 when I listed (thought I had) all combinations of the sums of ages. So I plonked for 1,4,9=14.

Thanks to other postings eg. #67 - (except 1,4,9=14 - not 15) it can be seen clearly that by seeing the bus number, Tom would only be perplexed if it was 13, thus solved by additional info. I wish I had spotted it myself.

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#129

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/12/2007 7:03 AM

I spent the weekend with friends. Their children all have piano lessons, aged 11, 9 and 6. Having overheard the lessons, I wouldn't say any of them truely play the piano (although the 9 year old is by far the best!)

Semantics!

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#130

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/12/2007 8:31 AM

I actually myself "played" at 6. My sister 10 had piano lessons and she bribed me to practice on her behalve. I was then sitting in front of the piano and doing scales and 'twinkle twinkle little star' etc and every body was happy. It stopped when she skipped a payment. (That is called Semitic).

The other time I overplayed my hand was when I decided to tune the piano into a honky-tonk. I really messed it up.

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#127

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/10/2007 6:41 AM

if my teacher would answer me with this riddle i would *(^*&*&^*&^(*%%%&%\$\$%)(\$R&^%\$&^%E#%^&\$&*(^()(*^*%^&*\$#%\$^# him!

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#131

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/12/2007 11:47 AM

This was stupid. The information given does not lead you to a positive answer. The answer given is simply one persons guess and the logic does not make any sense.

Anonymous Poster
#132

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/12/2007 2:57 PM

One of the strengths of mathematics is precision of expression. This teacher's inaccurate usage of "oldest" is more suited to a pub discussion than to a professional teacher of mathematics. Unfortunately, it is the only "rational" logically-based solution

Martha-Mae Titian (alias Fyz)

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#133

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/12/2007 3:03 PM

Playing piano at 9 has nothing to do with the answer. I have seen 4 or 5 years play piano. Also bus number 11 may be correct and why bus driver has to be a superstitious man. My answer is 2,3 and 6 years old.

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#134

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 1:37 AM
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#135

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 3:14 AM

I don't see the logic of a question with the answer attached to it.

I will have a look at it anyway because i like a challenge.

Posting it however seems useless.

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#136

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 3:18 AM

I am an identical twin in a family of 3 and I was born 8 minutes before my brother.

I am, therefore - The eldest! (and referred to as such by my family!)

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#148

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/14/2007 5:43 PM

In certain cultures the oldest child get everything, (Jacob in the Bible had to trick his brother and father to get the title.)

The youngest of twins in my neighborhood always complains about the discrimination at school. News letters and stuff are always given to the oldest and only child. He feels that he is missing out big time.

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#137

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 3:38 AM

If the number on the bus had been anything other than 13 then Tom would have known immediately how old all the children were.

Why?

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#143

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 8:08 AM

I tend to disagree with the answer. There is nothing that restricts the bus number to being 13!

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#145

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 8:56 AM

The statements:

"Well, if you multiply their ages together you get 36, and, if you add their ages you get the number on that bus."

There are only eight possible combinations of ages which when multiplied together give 36.

Are misleading because you are not "multiplying" the ages together, you are "adding."

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#146

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/13/2007 2:23 PM

Perhaps the ages are multiple together to get P (=36) , added to get Q , then the bus number is P + Q.

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#149

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/21/2007 3:32 PM

The solution given is paradoxical because it implies that Tom did not know if the children were (1, 6 & 6), or (2, 2 & 9), yet he knew that the children weren't (2, 3 & 6), (3, 3 & 4), etc.

Tom would have no proof to justify an assumption that John's statement was intended to have a unique solution, and that his piano comment was the final piece of information needed to make the answer unique.

The only way to give a single answer to this challenge is to make various societal assumptions, nothing engineering related.

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#150

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/22/2007 4:36 AM

It's all down to the number of the bus - read through the posts - there are lots which explain this - many by "Physicist?"

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#151

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

06/25/2007 11:58 PM

Just wanted to add that this is a great question with a perfectly correct and interesting answer. It's an old one, of course, but still well done.

Since I've been griping about lousy questions and half-formed answers on other threads, I figured I should praise the good ones, too.

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#157

### Re: My Teachers Three Kids: Newsletter Challenge (06/05/07)

07/12/2007 8:10 AM
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