Jumping Fleas

Geometry Level 4

In the plane, the points with integer coordinates are called lattice points. Suppose a flea in the plane jumps from one lattice point to another. Each jump is one unit to the right, one unit to the left, one unit up, or one unit down. If the flea starts at the origin and makes exactly 10 jumps, how many lattice points could possibly be the final landing place of the flea?

Details and assumptions

There is no restriction on which lattice points the flea can land on. As a specific example, the flea is allowed to make 5 jumps to the right, and then 5 jumps to the left to land back at the origin.

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