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Mathematics, 08.07.2021 18:20 fri90

Imagine a sphere, and a finite amount of points within this sphere, a point can only exist if you can get to it from the center in a number of steps. Each step is one fith the size of the diameter of the sphere, and can only go in the four cardinal directions, up, or down. Any number of steps can be taken as long as the point remains within the sphere. How many possible points are in this sphere?

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