Math puzzle

[LCHIEN]

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?

[TheRic]

Bus number 10

Ages 2,3,6

[jziegler]

Bus number 10

Ages 2,3,6

2+3+6 = 10?

2,3,6 are the ages, but the bus is 11

Jim

[TheRic]

Your right it's 11, added the wrong set of numbers.

[LarryG]

They could be aged 1, 2, and 18, which would make the bus number 21. Or 1, 4, and 9, which makes the bus number 14. Or 1, 3, and 12, which makes the bus number 16.

[mineengineer]

are there any twins*?

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

I must be missing something

[TheRic]

They could be aged 1, 2, and 18, which would make the bus number 21.

Technically correct. There are many combinations that use 1 for the age of one or more kids.

1, 3, 12
1, 6, 6
1, 4, 9
1, 1, 36 (could be twins, or less than 1 year apart).
etc.

[LarryG]

I assumed the part about the piano -- "the oldest plays the piano" -- was to preclude the possibility of there being twins with a younger sibling; i.e., ages 1, 6, and 6. I didn't even think about twins being younger; i.e., ages 2, 2, and 9.

And technically, even if the twins WERE the oldest, one of them would have been first-born, so "the oldest plays the piano" could still be true.

[LCHIEN]

There is one correct answer. You guys not reading the question carefully.

[radhak]

They could be aged 1, 2, and 18, which would make the bus number 21. Or 1, 4, and 9, which makes the bus number 14. Or 1, 3, and 12, which makes the bus number 16.

The way i see it, there could be more solutions where 3 numbers multiplied give us 36:

1+ 1+ 36 = 38
1+ 2+ 18 = 21
1+ 3+12 = 16
1+ 4+ 9 = 14
1+ 6+ 6 = 13
2+ 2+ 9 = 13
2+ 3+ 6 = 11
3+ 3+ 4 = 10
(that's just the math; please, nobody ding me for a 36 year old with 1-year-old twin siblings )

Now the only way to break this down further, is that the teacher said 'that bus', which means Tom could read the # on the bus. But if Tom is 'perplexed' that can only mean there's some ambiguity, which means the number on the bus is 13 (as any other #, and Tom would know the answer).

At this point, I am beginning to guess a bit - the piano comment has significance because of the 'oldest' as it eliminates the twin-6-year-old possibility. so the answer shd be 2,2,9.

(I am surer now that I typed it up; when I first thought of it, I hesitated because I recalled my 13-year-old twin nephews who have a constant wedge between them because one of them was born an hour earlier, hence has appended 'The Eldest' to his name, PO-ing his brother a lot )

edit : I took so long to type that up that I missed many replies in-between...

[Mrs. Wallnut]

is it 8?????? just took a guess at it...if that is wrong the answer is 34

[LarryG]

radhak is correct, I think ... Tom can see the bus, can presumably see the number, so if he's perplexed there must be two possible answers. Good thinking; good logic.

Problem is, it could still ... technically ... be either 2, 2, and 9, or 1, 6, and 6, for exactly the reason radhak states: one twin is always a little older than the other, but he would still be the oldest of the three (now we're getting some grammar into the math problem ...)

[LCHIEN]

The way i see it, there could be more solutions where 3 numbers multiplied give us 36:

1+ 1+ 36 = 38
1+ 2+ 18 = 21
1+ 3+12 = 16
1+ 4+ 9 = 14
1+ 6+ 6 = 13
2+ 2+ 9 = 13
2+ 3+ 6 = 11
3+ 3+ 4 = 10
(that's just the math; please, nobody ding me for a 36 year old with 1-year-old twin siblings )

Now the only way to break this down further, is that the teacher said 'that bus', which means Tom could read the # on the bus. But if Tom is 'perplexed' that can only mean there's some ambiguity, which means the number on the bus is 13 (as any other #, and Tom would know the answer).

At this point, I am beginning to guess a bit - the piano comment has significance because of the 'oldest' as it eliminates the twin-6-year-old possibility. so the answer shd be 2,2,9.

(I am surer now that I typed it up; when I first thought of it, I hesitated because I recalled my 13-year-old twin nephews who have a constant wedge between them because one of them was born an hour earlier, hence has appended 'The Eldest' to his name, PO-ing his brother a lot )

edit : I took so long to type that up that I missed many replies in-between...

Rad, That's the correct solution with the correct methodology.
I just thought it was a clever twist, the fact that the two combinations of possible ages added up to Bus #13 left Tom confused. But the added fact that there was an older eliminated the combo with two 6 Y.o.

I guess you have to take the perception that for most things, like skill in playing the piano, twins are basically considered to be the same age even tho there may be a few minutes or even hours difference in real age.

[LarryG]

I guess you have to take the perception that for most things, like skill in playing the piano, twins are basically considered to be the same age even tho there may be a few minutes or even hours difference in real age.

Unfortunately, that's what makes the puzzle flawed and, ultimately, a failure. There are two entirely legitimate, possibly correct answers. One twin always is older than the other, and this would make him the oldest of three children (grammar again). Even if one twin is considered the same age in years on the calendar, it doesn't preclude him being the actual oldest child of these three. And six-year-olds are old enough to play piano.

I'm sure the author of the puzzle intended 2, 2, and 9 to be the only possible correct answer, but ... he blew it.

[Tom Miller]

The reason Tom is perplexed is because John failed him in math, and apparently doesn't remember Tom can't count past two if he has mittens on.




Wow, I'm good at these -- give us another one!

Regards,
Tom