It's a mathematical function. Given the equation you are supposed to process in order to get your final number, it is irrelevant which numbers you choose. For example, look at the number 81 on the chart before you hit the magic button. Every time, this number will show you what sign will be revealed in the magic bubble. 72 is another one of these numbers. There is an entire series of numbers that will always be the result of the equation to be performed as per the instructions. Even though the signs are rotated, each number in this series will have the same sign as the others in the series.
I'll leave it up to someone else to reveal the formula to determine the predictable series of numbers.