Magic Gopher ~ How does this work?

[fishlipsmcgee]

This is spooky.   If anyone can you figure out how this works please let us know.  I know there is a logical explaination for this brain teaser. 


http://www.learnenglish.org.uk/games/magic-gopher-central.swf

[mascot]

It's simple math...dealing with the number 9.  If you look at all the 9 multiples they have the same symbol.  Any time you take a two digit number and add it up, then subtract from the original you end up with a multiple of 9.  Each time you try it they change the symbols next to 9, 18, 27, etc., just to throw you off so that each time you try it you have a different symbol.  But your number should always be divisable by 9.

tricky, but that's how it works!

[fishlipsmcgee]

Thanks Blind.      I knew there was a mathematical explanation for it and  I remember something similar from a math class but I couldn't remember the math behind it.  I noticed the symbols repeated.  I should have looked for a pattern and maybe I would have noticed that it was always nine.  It's a puzzle to have fun with if you don't have mathematically gifted friends who figure it out right away.   

[Teresa]

Try doing it quickly and not thinking about it - it's a matter of the number of symbols on the page at any one time - most of them are one symbol and the chances are that symbol is the one that your number adds up to. 

[karen J]

There is another trick with the 9's, one that I learned from Renee K on the old board. Using your ten fingers, fold your left pinky in. The resulting nine fingers showing represents 9 x 1 (9 fingers). Fold your left ring finger in, and that is 9 x 2 (one finger showing on left, second finger down, 8 fingers on right. Fold your third finger on left down, and you'll have 2 fingers on the left of that, and seven fingers on the right (27).
I can't explain it very well, but hope you get the idea.

I liked that gopher, and so did my daughter. Even after reading Blind Too's explanation, I still can't figure out how they got the same symbol every time.

[Teresa]

Karen - pick one number (multiple of nine) and look at it thru several tries of the game.  You'll see that the symbol by that number is different each time and each time, that is the symbol displayed. 

If you take a two digit number and transpose the digits, the difference is a multiple of nine.  In other words, if you take 43 and flip the digits to get 34 the difference between the two numbers is 9.  If you subtract the sum of the two digits of any number from that number, you'll get a multiple of nine.  So, your answer to their little math problem is generally going to be a multiple of nine.  All of those have the same symbol . . . . which is the one displayed when you get to that point.

I hope that makes more sense to you than it sounds like it does to me.

[karen J]

I hope that makes more sense to you than it sounds like it does to me.

Actually, yes it does make sense. I think I will sit down with Laura and have some fun with it.