The Grasshopper

Consider an infinite grid of squares. A grasshopper sits on one of the squares. The grasshopper can jump two squares in any horizontal or vertical direction, and it can jump to the adjacent square diagonally. Can the grasshopper ever reach a square that is adjacent to its starting square by a side?

Difficulty level (1 very easy - 10 very hard): 2

Topics:
Combinatorics -> Combinatorial Geometry Combinatorics -> Invariants Combinatorics -> Colorings -> Chessboard Coloring
Sources:
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