I just love stuff like this!

[emmagrant01]

One of my cousins sent me the URL below, which shows a mathematical "magic trick".

http://mr-31238.mr.valuehost.co.uk/assets/Flash/psychic.swf

It's pretty slick, but it's easy to figure out how it works. I'm such a geek -- yes, I did spend my lunch break figuring this out... :^P

I'll hide the solution behind a cut. Impress your friends!





All right, first of all, consider all of the two-digit numbers whose sum is, say, 7. They are 7, 16, 25, 34, 43, 52, 61, and 70. What do they all have in common? They are all 9 apart. (Subtract any two of them and the difference will be a multiple of 9.)

Do this with any other number, and the same thing will happen. For example, the numbers whose digits add to 12 are 39, 48, 57, 66, 75, 84, and 93. Again, all a multiple of 9 apart.

So why is the 9 important? Well, when you take a number N, whose two digits are A and B, notice that you can write N = 10A + B. (Example: 84 = 10*8 + 4, so A=8 and B=4). The instructions say to subtract the sum of the digits from the number you started with, N - (A + B). We can do this using simple algebra to get 10A + B - (A + B) = 9A. So, the answer will ALWAYS be a multiple of 9. That is, when you do this problem, you'll always get as your answer either 0, 9, 18, 27, 36, 45, 54, 63, 72, or 81. It turns out that you'll never get an answer bigger than 81, since 90 - 9 = 81, 91 - 10 = 81, 92 - 11 = 81,... 99 - 18 = 81.

Now go back and look at the web page. Look at all of those numbers with the symbols. You'll notice that all of the mulitples of 9 between 0 and 81 have the SAME symbol. Click the crystal ball and you'll get that symbol. When you look at the web page again, notice that the symbols have all changed, but it will still be the case that all of the multiples of 9 will have the same symbol. Click the crystal ball again and now you'll see that symbol. They have to change it every time so you won't get suspicious, and it's done very cleverly. The symbols that are not on the list above don't seem to change, so you don't notice it.

Anyway, that's how it works! I love this stuff!

Comments

[helens78]

You are so cute! And that's a very cool trick. :) (Have you ever noticed how most of the best "mind tricks" are math tricks?)

[jedirita.livejournal.com]

My mom just sent me this puzzle, too. I figured out that the answer would always be a multiple of nine (though I didn't know that funky algebraic explanation), but... I have NEVER been able to open that website! The Intenet hates me! Why won't it open for me? Oh, why????