# 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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