Mysteries of the crystal ball revealed!
 

Crystal Ball

Try it a few times. Freaky? Good. Now, tell me if you figure it out. I think I've got it, but I want to see how easy it is for someone else to get it. It takes a little observation, but thats all I'll let on about it...

It has to do with multiples of 9, as all the multiples of 9 listed on the chart have the same symbol. Try the trick with any two digit number, you get a multiple of 9 as the answer. I believe it is because we use a base 10 numbering system, and 9 is the highest single digit in that system. If you try the same trick with base 8 or base 6, you get the same sort of results (with multiples of 7 and 5, respectively).

Oh that's a subtle trick but not that hard to see through. If you really want to know how it's done then highlight this: The only possible numbers that can result from doing what they ask are: 81,72.,63,54,45,36,27,18,and 9. A quick check confirms that all those numbers have the same symbol and thus it is always correct.

Edit: and I was beat to posting.

It still gives a nice shock at first apparition.

Wrong.

EDIT: Silly me. One word post. pheh. Sorry guys, it was late, and I forgot.

Basically you start with 10. It can be shown that 1 + 0 equals 1 and 10 minus 1 equals 9. Now since adding 1 to make it 11 adds 1 to both the sum of the digits and the number itself the number you get doesn't change. Now once you increase to 20 you're adding 10 to the numer and an extra one to the sum that you subtract from it. In other words 20 - (2+0) = 18 or 10 - (1+0+1) +10 =18. The same thing happens when it increases to 30 that is 10 more to the number and 1 more to the sum. This has to do completely with the fact we are using a base 10 system and the operation being used. Noting this it's a small matter to make sure that the numbers generated this way have the same symbol. Don't believe go check.

Yeah, that's like what I said, but with more math in it. But basically I'm still right. and first.

If that were true, wouldn't the same symbol have to be shown in the ball each time? Even if you figured it out that quick, its still cool.

The symbols are randomly changed each time you restart the thing. It scrambles what symbols are where. The one shared by those numbers changes but the all always share the same symbol. It's a nifty piece of programing.

Yeah, that's the extra bit I was lookng for. Neato, huh?