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Magic Gopher Explanation
When you follow the instructions, your number goes through the following formula: xy - (x+y), where x is the first digit, and y is the second. (For example, for 53: x = 5 and y = 3... -> 53 - (5+3) = 45.
This formula always produces multiples of 9 (0, 9, 18, 27, 36, 45, 54, 63, 72, 81). If you look at the symbol chart, the symbol for multiples of 9 are always the same, but the chart itself changes every time you play again. Next time you see the symbol chart, look at the symbol for 9. Any number that you originally picked will result in that symbol.
The math sequence is set up so that each answer is a multiple of 9. Then, all the multiples of 9 are set by the same symbol. Each round, the multiples of 9 are put next to a different symbol.