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# Ants on Marzo

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An ant is crawling on the planet of Marzo, which is a perfect sphere with radius $10^{33}$ yoctometers. Every day, the ant crawls $10^{14}$ yoctometers south, $10^{14}$ yoctometers east, then $10^{14}$ yoctometers north. Let $N$ be the set of
all points such that the ant returns to its starting place.
Jacob chooses a point in $N$ at random, and if $N$ is empty,he writes $-1$.
If $N$ only has one element, Jacob always chooses that element.
If $O$ is the center of Marzo, $S$ is the south pole, and $A$ is the point Jacob chooses, he writes down $\lfloor 10^{26}\angle SOA\rfloor$, in radians.
If $\pi=3.1415926535897932384626433832795$, then what is the smallest possible number Jacob can write down?

Mar 9, 2021