MathDB

Johann and Nicole are playing a game on the coordinate plane. First, Johann draws any polygon

\mathcal{S}

and then Nicole can shift

\mathcal{S}

to wherever she wants. Johann wins if there exists a point with coordinates

(x, y)

in the interior of

\mathcal{S}

, where

x

and

y

are coprime integers. Otherwise, Nicole wins. Determine who has a winning strategy.

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