[Musicforawhile (OP)]

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 (OP)]

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?

[alancalverd]

Sorry it has to be equations, but life is too short for words!

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"

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 (OP)]

I take it you're a mathematician []. Those equations were easy enough to follow, thank you.

[Musicforawhile (OP)]

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.

[David Cooper]

From www.mathisisfun.com

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

[Musicforawhile (OP)]

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 (OP)]

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.

[David Cooper]

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]

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.

[jeffreyH]

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]

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.

[CliffordK]

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 (OP)]

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

Is this humour..?

[jeffreyH]

So what is the next letter in this sequence?

EEAAUA

[alancalverd]

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 (OP)]

Can you give a clue with the FMAMJJA puzzle?

[David Cooper]

I thought FMAMJJA looked familiar, and now I remember why. Add another three letters and a five-letter name appears.

[jeffreyH]

You need to add another 5 letters.

[David Cooper]

Two of the five are already there.