Math Is Fun Forum

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Ages problem

Two matematicians meet, they were college mates who hadn't seen each other for a long time, so they start discussing trivia:

Math. A: I have a wife and three kids now.

Math. B: Bet I can guess the kid's ages if you'd give me a clue.

A: The product of the ages equals 36.

B: Another clue?

A: The sum of the ages equals the number of THAT house.

B: Just one more?

A: Alright. My oldest son plays the piano.

Try to figure this out.:/

Last edited by Ubergeek (2009-07-25 09:16:15)

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ages problem

Hi Ubergeek;

(9,2,2) are the ages of the three kids

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Ages problem

I got the same answer as Bobby. Nice logic...took me a while to spot.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Ages problem

I love this type of puzzle!

I first saw it in one of Martin Gardner's books (back in the Jurassic Period).
The solution does not require extensive Algebra, just some Common Sense.

For those not familiar with the approach, here it is . . .

The product of the three ages is 36.
There are several sets of three factors with a product of 36,
. . so Math B needed more information.

He was told that the sum of the ages is that house number.

He made this list:
. . .

Since Math B could see that house number, he would immediately know the ages.

But he needed more information.
This means that the sum was duplicated on the list: (1,6,6)=13 , (2,2,9) = 13

The final answer established that there is an oldest boy.

Therefore, the ages are: 2, 2 and 9.
.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Ages problem

Yes...I like this kind of puzzle too. Can't always get them because of their devious construction, but they're a fun challenge!

I'd made a similar "sums" list of the combinations of the factors of 36, which revealed the "13"-duplication and thus answered the second clue. However, I wasn't sure that "oldest" necessarily ruled out 1,6,6...until I looked at it more mathematically: ie, that 6=6, clearly leaving 2,2,9 as the intended answer.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Re: Ages problem

Glad you liked it guys.:D

Here's another one: (though is not only common sensical I guess)

A couple has sons and daughters. Each son has as much brothers as sisters. Each daughter has as much brothers as twice the sisters. How many kids does the couple has?

Have fun.

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Re: Ages problem

Even another one:

If 5 cats catch 5 mice in 5 minutes, 100 cats will catch 100 mice in how many minutes?

Just one more:

Is there a mathematical number or equation or concept you can't define in less than 100 words?

Last edited by Ubergeek (2009-07-27 14:35:53)

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ages problem

Is there a mathematical number or equation or concept you can't explain in less than 100 words?

Yes, I can't explain anything in less than 100 words.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

quittyqat

Member

Registered: 2009-04-08

Posts: 1,215

Re: Ages problem

Two matematicians meet, they were college mates who hadn't seen each other for a long time, so they start discussing trivia:

Math. A: I have a wife and three kids now.

Math. B: Bet I can guess the kid's ages if you'd give me a clue.

A: The product of the ages equals 36.

B: Another clue?

A: The sum of the ages equals the number of THAT house.

B: Just one more?

A: Alright. My oldest son plays the piano.

Try to figure this out.:/

I've heard this puzzle before, just with sisters.

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I'll be here at least once every decade.

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Re: Ages problem

Is there a mathematical number or equation or concept you can't explain in less than 100 words?

Yes, I can't explain anything in less than 100 words.

I'm sorry, there was a mistake at my question, now I fixed it.

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ages problem

Hi Ubergeek;

No problem, I was trying to be funny.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

quittyqat

Member

Registered: 2009-04-08

Posts: 1,215

Re: Ages problem

Even another one:

If 5 cats catch 5 mouses in 5 minutes, 100 cats will catch 100 mouses in how many minutes?

Just one more:

Is there a mathematical number or equation or concept you can't define in less than 100 words?

It's mice, not mouses.

Last edited by quittyqat (2009-07-27 11:39:02)

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I'll be here at least once every decade.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ages problem

A couple has sons and daughters. Each son has as much brothers as sisters. Each daughter has as much brothers as twice the sisters. How many kids does the couple has?

Last edited by bobbym (2009-07-27 20:59:59)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Ages problem

I solved Q2 & Q3, but not Q4.

However, googling for Q4 dug up something that looks related, but I had to give up on trying to understand the 'explanation' when I began to see stars and I heard "tweet, tweet".

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Re: Ages problem

Q4. Is it something to do with Berry's Paradox? If so, my brain says "good night".

I don't know Berry's paradox. But the answer to Q4. is

.

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Ages problem

But the answer to Q4. is

.

No point in asking for an example of one, then.

But could you explain your answer for me, Ubergeek?

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Re: Ages problem

But the answer to Q4. is

.

No point in asking for an example of one, then.

But could you explain your answer for me, Ubergeek?

Yes, see,

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Ages problem

Yes, see,

Oh...I see!!?! At least, I hope that my vision will return after I can uncross my eyes again!

Your explanation is quite in keeping with how that fella in your signature defines mathematics...and also seems to follow Berry's Paradox.

This Wikipedia article - http://en.wikipedia.org/wiki/Berry_paradox - begins by saying:

The Berry paradox is a self-referential paradox arising from the expression "the smallest possible integer not definable by a given number of words." Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry (1867-1928).

All too much for my little brain!

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Ubergeek

Member

Registered: 2009-07-14

Posts: 205

Re: Ages problem

Your explanation is quite in keeping with how that fella in your signature defines mathematics...and also seems to follow Berry's Paradox.

Yeah, he knows what he's talking about, believe me, he's brilliant, I suggest his book "The Scientific perspective" if you wanna check his work someday, which I finished reading yesterday .

This Wikipedia article - http://en.wikipedia.org/wiki/Berry_paradox - begins by saying:

The Berry paradox is a self-referential paradox arising from the expression "the smallest possible integer not definable by a given number of words." Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry (1867-1928).

All too much for my little brain!

Thanks for introducing Berry's paradox to me.

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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

momofmathkid

Member

Registered: 2008-01-14

Posts: 32

Re: Ages problem

9,2,2 are the ages