Hi gopher-loving Friends,
As Oxygen said, the only numbers you can ever get as answers are 9, 18,
27, 36, 45, 54, 63, 72, and 81 ... that is, multiples of 9. And the chart
symbols for all numbers which are multiples of 9 are the same, so that
Mystic Gopher always gets it right.
To understand why this works, read on ... (spoilers ...)
The reason why this works is because of our base-10 number system.
Let "a" represent the first digit in your two digit number, and "b" represent
the second digit. Then, your two digit number would be expressed as:
(10 times a) plus b
For example, if your number is 49, then a = 4, and b = 9, and indeed, 49 =
(4 times 10) plus 9.
Notice, what happens when you go through the operation that Mystic
Gopher asks of you:
1. Choose a two-digit number:
(10 times a) plus b
2. Add the two digits together:
a plus b
3. Subtract the answer from the original two-digit number:
[(10 times a) plus b] minus [a plus b]
And if you remember your algebra, simply distribute, re-arrange, and
solve:
10a + b - (a + b)
= 10a + b - a - b
= 10a - a + b - b
= 9a
So, no matter what number you choose, the final answer will always be NINE
times an integer, that is, a multiple of 9.
Wha la!
HF
