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John Simkin

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.)

Edited by Kathy Beckett

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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.

Edited by Kathy Beckett

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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 be less 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.

Add the digits {a+b} 2+8=10

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? :ice

Edited by Kathy Beckett

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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.

Add the digits {a+b} 2+8=10

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? :ice

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