Challenge Questions

There should have been at least three interpretations - the number marked on the bus (usually referred to as the number of the bus where I live), the number of passengers on the bus, or the number of people on the bus including staff. That would have been perplexing. If we allow all three, we would have had no way of finding a solution. If we eliminate the number of the bus (because the maths teacher appears to be a pedant), then we could assume the two possible numbers differ by one...

Fyz

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

ages 6-3-2 Bus number 11

Tigermaster

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

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

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

RF

Never is when you copy.

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

"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?

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

I agree - Randall must be slipping...

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

Quick , hide.

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.

Well look tha ealder child has 9

and other's are 4,1 aged

Bus number:14

the answer is :

3,3,4. Bus is 10

Especially: "an easier number puzzle..."

Point taken, I hope

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.

<sulk>

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

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>

Which leaves the replies to that input rather incomprehensible

Indeed it does !

<annoyance on>

Q: How many seconds does it take to google an answer.

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>

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

I am drooling and dribbling with delight ! I do this normally , but on this occasion it is with pure delight.

What I tried to post yesterday was <spoiler> - there are many different endings to this riddle on the web. Yours is far and away the best fyz.

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)

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

<applause>

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

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

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

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

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

Isn't it more likely the youngest is Toms ?

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

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.

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.

Twins with different fathers has been known.

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

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.

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.

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.

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.

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!

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.

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

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.

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)

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.

Nadeem Butt

If you found this too easy try this :-

http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=puzzle086

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.

Still a load of rubbish!

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!)

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.

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?

Cheers

Gareth

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

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."

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

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.

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

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.

Fitz

Episode 8 is up.