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# Magic Gopher

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Yes. Each number generated by what they ask you to do is a multiple of 9.

The reason why the gopher is always correct is that he changes the symbol each time you play.

Look at all of the multiples of 9--they always have the same symbol, and when you play again the new symbol board will have identical symbols for 9 as well.

This threw me for a loop for a minute.

Kathy

(The number 90 is excepted,and bears a different symbol, as it is too high to generate with the rules given.)

Funny, the gopher isn't always correct. Try always thinking of 43 for example.

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Another little item with this game:

Since a double digit number is 10 times some number {a} plus the single digit {b}, the double digit number looks like this:

10{a} +b

0<a<10, b<10

Since we know that in order to generate the new number, we have to subtract the addition of the digits from the original number:

10{a}+b -- {a+ b} = 9{a}

And because the gopher works on multiples of 9, to generate the new number for use on the symbol board, just use the value of {a} multiplied by 9 to go directly to that new one.

Saves a little time.

Kath,

I played the game and still surprised at how it is done...and still haven't understood anything from your explanation.

But of course, for a math genius(!) like me, it is normal.

See the example dialogue between my mom and me that took place two days ago.

Mother (on the phone): Aren't you late for class?

Me: No, it's only ten past eight now. If I leave home at five past eight, I'll be at school on time.

Mother: So you'll travel in time then!?

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10{a}+b is the "setup" for a double digit number.

{a} cannot = 0 and must not be greater than 10.

If {a}=0, then 10{0} +b= 0+b, which is a single digit.

I{a}=10, then, 10{10}+b= 100 +b, which is three digits.

I'll pick a number and set it up for you, say 51.

51=10{5}+1

a=5 and b=1 Add these digits {a+b} 5+1=6

Next,we have to subtract the sum of our digits from the number we chose.

51-6=45.

Written another way,

10{5}+ 1-{5+1}=9{5}.

but if you can see the value of a, then you can multiply that value by 9, instead of adding and subtracting.

Let's try another one.

28=10{2} +8.

Subtract this off of 28, our original number.

28-10=18 or 9{2}

So just set up your original number as 10{a} +b, and multiply {a} times 9.

This works because

10{a}+b-{a+b}=9{a}

And each time you play anew, the symbols on the board change--look at all the multiples of 9,they are all the same symbol, except 90 (which could not be generated according to the rules.)

Is this better, Cig?

So, the key to this trick is number 9, yes?