# The Naked Scientists Forum

### Author Topic: Fun maths problems  (Read 9642 times)

#### Musicforawhile

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##### Fun maths problems
« on: 07/11/2014 22:16:58 »
Hi, so in the book 'The curious case of the dog in the night-time,' I came across the puzzle about the three doors with the prize behind one door. You are supposed to choose two doors then you should change your initial choice after the first door you pick is a dud. Something like that I think...

Do you know any other maths problems or puzzles that a non-mathematician would enjoy and have a sort of 'fun' context?

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #1 on: 10/11/2014 16:41:18 »
For non-mathemticians like me who like puzzles:

The Puzzle:

There are 2 trees in a garden (tree "A" and "B") and on the both trees are some birds.

The birds of tree A say to the birds of tree B that if one of you comes to our tree, then our population will be the double of yours.

Then the birds of tree B tell to the birds of tree A that if one of you comes here, then our population will be equal to that of yours.

Now answer: How many birds in each tree?

« Last Edit: 13/11/2014 12:36:36 by Musicforawhile »

#### alancalverd

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##### Re: Fun maths problems
« Reply #2 on: 10/11/2014 17:44:16 »
Sorry it has to be equations, but life is too short for words!

Quote
The birds of tree A say to the birds of tree B that if one of you comes to our tree, then our population will be the double of yours.

in other "words"         A + 1 = 2 x (B-1) = 2B - 2   call this "equation 1"

Quote
Then the birds of tree B tell to the birds of tree A that if one of you comes here, then our population will be equal to that of yours.

i.e.       B+1 = A-1   call this "equation 2"

If we subtract 1 from each side of the equation 2, then B = A-2  (equation 3)

Now we have a value for B, so put this value back into equation 1

A + 1 = 2 x (A-2) - 2 = 2A -6

Subtract A from both sides

1 = A - 6

So A = 7

And B = A - 2 according to equation 3, so B = 5

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #3 on: 10/11/2014 18:08:03 »
I take it you're a mathematician . Those equations were easy enough to follow, thank you.

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #4 on: 10/11/2014 19:40:42 »
The Puzzle:

Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.

« Last Edit: 13/11/2014 12:36:16 by Musicforawhile »

#### David Cooper

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##### Re: Fun maths problems
« Reply #5 on: 11/11/2014 18:08:43 »
From www.mathisisfun.com

Promotion of a website is one thing, but this link looks as if it goes to a terrorist organisation.

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #6 on: 12/11/2014 00:06:14 »
I am not trying to promote it, I just wanted to cite my source. But I suppose it doesn't really matter, it's not going to be plagiarism really. Terrorism?

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #7 on: 12/11/2014 00:10:36 »
The link was bad if that's what you meant by terrorism. I missed out an 's' by accident.

And I'm not plugging them, I have nothing to do with them. But I didn't make up the puzzle. So just referencing the source.
« Last Edit: 13/11/2014 12:37:34 by Musicforawhile »

#### David Cooper

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##### Re: Fun maths problems
« Reply #8 on: 12/11/2014 17:19:47 »
It wasn't a missing "s", but an extra "i", the result being "isis". As for promoting a website by repeating (or attempting to repeat) a link to the same site so soon in a thread like this, you make it look as if you might be promoting it (even if you actually have nothing to do with the people behind it), and that risks making them look bad, so this is something we always need to be careful to avoid doing.

#### alancalverd

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##### Re: Fun maths problems
« Reply #9 on: 12/11/2014 17:50:39 »
Yes, it's a terrorist organisation. "....intimidation....spreading despair....causing physical harm..."

I've now spent 2 days trying to drive, work, and play music whilst figuring out the "10 digit" puzzle in my head (no, I'm not a mathematician!) and I have come close to maiming or frying most of the population of southern England during the day, then spreading despair among musicians and conductors in the evenings. Tomorrow I'm going to sit down with a pencil and paper and do it properly, because I have no intention of flying whilst my mind is so preoccupied.

The stain of guilt lies with the perpetrator. May the Lord have mercy on your soul, Sir or Madam.
« Last Edit: 12/11/2014 23:19:17 by alancalverd »

#### jeffreyH

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##### Re: Fun maths problems
« Reply #10 on: 13/11/2014 01:23:12 »
Yes, it's a terrorist organisation. "....intimidation....spreading despair....causing physical harm..."

I've now spent 2 days trying to drive, work, and play music whilst figuring out the "10 digit" puzzle in my head (no, I'm not a mathematician!) and I have come close to maiming or frying most of the population of southern England during the day, then spreading despair among musicians and conductors in the evenings. Tomorrow I'm going to sit down with a pencil and paper and do it properly, because I have no intention of flying whilst my mind is so preoccupied.

The stain of guilt lies with the perpetrator. May the Lord have mercy on your soul, Sir or Madam.

6210001000

#### alancalverd

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##### Re: Fun maths problems
« Reply #11 on: 13/11/2014 08:27:27 »
The world is a safer place, music lovers will be grateful, and perhaps I'll earn some money today instead of gazing vacantly into space.

I was getting there by inspiration and elimination (though the bandleader called it "gasping and farting in the tuba section"), but it would be interesting to see an algebraic solution.
« Last Edit: 13/11/2014 08:29:36 by alancalverd »

#### CliffordK

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##### Re: Fun maths problems
« Reply #12 on: 13/11/2014 10:22:09 »
Ok,

Here is one of my favorite math-ish puzzles that I bumped into a while ago.

What is the next letter in the sequence?

FMAMJJA

(once you have the right answer, you will KNOW that it isn't a guess).  Thus, no need to post the answer either (and definitely not the "key").

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #13 on: 13/11/2014 12:41:27 »
The stain of guilt lies with the perpetrator. May the Lord have mercy on your soul, Sir or Madam.

Is this humour..?

#### jeffreyH

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##### Re: Fun maths problems
« Reply #14 on: 13/11/2014 22:33:03 »
So what is the next letter in this sequence?

EEAAUA

#### alancalverd

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##### Re: Fun maths problems
« Reply #15 on: 13/11/2014 22:54:50 »
The stain of guilt lies with the perpetrator. May the Lord have mercy on your soul, Sir or Madam.

Is this humour..?

It certainly ain't science, nor great literature, so, my dear Watson, we are inevitably led to the conclusion that it is what earth-people call humour.

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #16 on: 14/11/2014 15:26:27 »
Can you give a clue with the FMAMJJA puzzle?

#### David Cooper

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##### Re: Fun maths problems
« Reply #17 on: 14/11/2014 17:35:35 »
I thought FMAMJJA looked familiar, and now I remember why. Add another three letters and a five-letter name appears.

#### jeffreyH

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##### Re: Fun maths problems
« Reply #18 on: 14/11/2014 20:46:31 »
You need to add another 5 letters.

#### David Cooper

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##### Re: Fun maths problems
« Reply #19 on: 14/11/2014 20:50:26 »
Two of the five are already there.

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #20 on: 14/11/2014 21:06:23 »
The answer to the ten-digit problem is:

6210001000

#### Musicforawhile

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##### Re: Fun maths problems
« Reply #21 on: 14/11/2014 21:08:10 »
Is it a number puzzle or letter puzzle?

#### alancalverd

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##### Re: Fun maths problems
« Reply #22 on: 14/11/2014 23:16:33 »
The answer to the ten-digit problem is:

6210001000

True enough, but is there a logical or algebraic approach to the solution?

#### David Cooper

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##### Re: Fun maths problems
« Reply #23 on: 14/11/2014 23:22:27 »
Is it a number puzzle or letter puzzle?

FMAMJJA should not be approached as a mathematical problem.

#### chiralSPO

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##### Re: Fun maths problems
« Reply #24 on: 14/11/2014 23:47:10 »
Is it easier if posed as JFMAMJJA... ?

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##### Re: Fun maths problems
« Reply #24 on: 14/11/2014 23:47:10 »