Math Answers

My son (14) asked how [Magic Gopher] works. He tried several times to stump them, with no luck. He wanted to know he mathematical method for "guessing" the numbers. I'm sure it's a very simple and logical process, but I have no answer.

Can anyone help? Thanks.

Joyce knows!

It's the magic of our base 10 system :-)

Basically what you're doing is eliminating the second digit and then subtracting the first digit from 10 times the first digit which always give 9 times the first digit. On the Egyptian chart at the end, all the multiples of 9 always have the same symbol next to them. [Sandra note: All except the nines are just random dummy-art because only the multiples of nine will be "the answer." The program changes the symbols on the chart each time you play the game.]

Algebraically it goes like this ...

If a number looks like ab, it would be represented algebraically as:

10*a + b.
So for:

12 then a=1 and b=2 so 12=10*1 + 2
37 then a=3 and b=7 so 37=10*3 + 7
82 then a=8 and b=2 so 82=10*8 +2

In the first step of the game they ask you to add a and b together.
And then they tell you to subtract that number from the original number.
That's just a way of eliminating the last digit so all problems turn into:

10*a + b - (a+b)
rearranging, you can see that the b part of every 2 digit number gets eliminated:
10*a - a + b - b
So all problems turn into either 10-1, 20-2, 30-3, 40-4 ...

10*a - a = 9a

10*1 - 1 = 9*1 = 9
10*2 - 2 = 9*2 = 18
10*3 - 3 = 9*3 = 27

and so on. So all two digit numbers are turned into 9 times the first digit of the number.

Joyce

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