Two powerhouses of history go head to head. Leonhard Euler starts. Carl Friedrich Gauss plays second. They have a $6\times 6$ grid. Each turn a player places a domino (a $1\times2$ or $2\times1$ rectangle). Dominoes cannot overlap, and the first player who can’t place a domino loses.
We will assume they are both perfectly intelligent (trivial result) and know the best strategy. Who wins?
Generalisation to $n\times n$ grid?
Since Gauss is smart, he would probably figure this out:
Let the points with integer coordinates be the vertices of the grid, with the origin corresponding to the center. Gauss should use this strategy from the start of the game: If Euler places a domino centered at coordinates $(x,y)$, Gauss should play at coordinates $(-x,-y)$. If such a move was not allowed, then Euler's move would not have been allowed either. Therefore, Gauss makes the last move and wins. For the second question, if $n$ is even, then Gauss can use the same strategy and win. I don't know the solution when $n$ is odd.