How many discs?

I was playing Towers of Hanoi. The game consist of a certain number of discs of different sizes that i have to move from stick \(A\) to stick \(C\), in such form that in no moment of the game a disc that is bigger than other is above from it.

I was playing with \(N\) discs, i made a perfect game. If I counted \(127\) movements. What is the value of \(N^2\)?

Note:

  • A perfect game is considerated to do the minimum quantity of movements.
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