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Discussion Starter #1

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David,

I'll bet you that every time you play your final result is either 0 or a multiple of 9 up to 9^2 :). Check the symbol next to zero before clicking the magic ball - that will be the answer every time ;).

[edit to add] Upon further study and digging up some OLD brain cells - since initial number is two digits. 0 is never an answer. Lowest number than can be chosen is 10 w/ final result being 9. Greatest number than can be chosen is 99 with final result of 81 - all multiples of 9. There was some principle I learned in high school accounting about finding errors when balancing the books - had to do if # was divisible by 9 but my CRS is acting up, can't remember the name!

I can't explain why 0 always has the right symbol unless the author is trying to account for 'cheaters' - someone who thinks of any # < 10 as a two-digit number (like 09 or 08 - any number below 10 and the result will always be zero). Thanks Dale for helping me kick into analytic mode :)![/edit]
 

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...that would be a transposition error - reversing 2 numbers will always result in a difference that is divisible by 9. Example: if you write down 528, but really meant 582, you'll be off by 54, which is divisible by 9.
 

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Yep, I was playing around with it and saw that that is the trick. Every time the choices of numbers that can possibly be the answer all have the same symbols. The symbol changes every time you try again, but always 0, 9, 18, 27, 36, 45, 54, 63, 72, 81 will always have the same symbol, and that is the one which will come up in the ball when clicked. If you add and subtract correctly, those are the only numbers that can be answers. I did notice he has a couple of the same symbol scattered around amonst other numbers to throw you off so it won't be readily apparent what the trick is.

And yes, I had used numbers with the first digit being "0".
 

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I started to Google it to see if I could find something like that, but being an engineer, with the inquisitive mind that usually goes with that, I just had to figure it out myself.

First I tried to do a couple of the numbers "backwards", and that led me to the conclusion that many of the numbers in the chart were just fluff and could not be arrived at, so that led me to the "trick". I pretty quickly "discovered" the small number of answers actually viable.

A mathmetician would probably know it right off, but math was not my best subject, until I got to Trig., which I did very well at. Anything "spatial" was pretty easy to me, but Calculus stopped me dead in my tracks. Could not "see" that in my mind like I could geometry and trig. Funny how we all differ so much, I had a good friend who was an absolute wizz at Calculus, but had a hard time with medium level Trig.
 
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