The Wonder of Mathematics

[T_G]

The Wonder of Mathematics :-Jumbo


Multiply of 37 by multiplies of 3:

3 x 37 = 111
6 x 37 = 222
9 x 37 = 333
12 x 37 = 444
15 x 37 = 555
18 x 37 = 666
21 x 37 = 777
24 x 37 = 888
27 x 37 = 999
Nice one:

111.111.111 x 111.111.111 = 12.345.678.987.654.321

Trapeze:

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111

another Trapeze:

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

and another one:

0 x 9 + 8 = 8
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
987654321 x 9 - 1 = 8888888888
9876543210 x 9 - 2 = 88888888888

 

[spiney]

Hmmm, what prompted this?

There's many such mathematical tricks and recreations, eg "casting out nines", "magic squares", etc. In old books. Also much discussed by Martin Gardner:

see: www.g4g4.com .

also: http://en.wikipedia.org/wiki/Martin_Gardner .

(here's a specific magic squares link: www.markfarrar.co.uk/msfmsq01.htm ).

Such stuff not so popular now, as people prefer computer games, or maybe Soduku (personally, I'd rather just eat raw fish, it's more fun!).

That's not mentioning the abstruse topic of number theory:

see: www.mathpages.com/home/inumber.htm .

Internet security - data encryption - relies heavily on number theorems, and of course there's people working feverishly on cracking techniques ....

 

[Llew]

OK let's keep it simple - What's the last number that can be written down in words (using the conventional system of writing English numbers) without repeating the same letter?

Llew

 

[spiney]

OK let's keep it simple - What's the last number that can be written down in words (using the conventional system of writing English numbers) without repeating the same letter?

Llew

Well, Llew, I'm probably wrong, but is it Five Thousand?

 

[Llew]

You got it spiney. Once you've got a thousand, nothing else it can be.

 

[spiney]

Well, Llew, must admit I cheated!

I knew it was a "typical known problem", so used Google to find it. Took some fiddlng to get suitable search words, but it worked.

I'm a spoilsport, sorry, but for anyone who likes this stuff there's loads "out there", just Google search using the word "puzzles"!

 

[T_G]

Hmmm, what prompted this?

I just got it in a mail and it looked interesting to me...I did not find all of this in my spare time trying to solve some age old problems

 

[spiney]

OK let's keep it simple - What's the last number that can be written down in words (using the conventional system of writing English numbers) without repeating the same letter?

Llew

However .......

Llew, would "sixty cubed" also be an acceptable answer, or do you consider that cheating?

(Worked this answer out all by myself, but then needed three asprin!).

 

[spiney]

Quote:
Originally Posted by spiney
Hmmm, what prompted this?


TG: I just got it in a mail and it looked interesting to me...I did not find all of this in my spare time trying to solve some age old problems
__________________

No criticism implied, in fact the opposite, I only wondered .....

I'd say, thinking up stuff like this is horribly difficult, and if you do manage it, then no doubt the same puzzle already exists somewhere (that's how I answered Llew ....).

I don't really like these types of puzzle, probaby because i'm no good at them .......

 

[Llew]

However .......

Llew, would "sixty cubed" also be an acceptable answer, or do you consider that cheating?

(Worked this answer out all by myself, but then needed three asprin!).

Naughty but nice - although it's really a mathematical expression needing a solution, isn't it?

Llew

 

[spiney]

Naughty but nice - although it's really a mathematical expression needing a solution, isn't it?

Llew

Well, Llew, I think it's a question of "sense and reference" - in Frege's/Russell's usage - ie, two logical expressions having different meanings, but nevertheless "pointing at" the same object!

(there, that should "get me off the hook", tee hee hee ..... oops!).