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Omni-MATH / Bob is coloring lattice points in the coordinate plane. Find the number of ways…

Problem

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problem

Bob is coloring lattice points in the coordinate plane. Find the number of ways Bob can color five points in {(x,y)∣1≤x,y≤5}\{(x, y) \mid 1 \leq x, y \leq 5\} blue such that the distance between any two blue points is not an integer.
Plain-text mathematical notation (without MathML)
Bob is coloring lattice points in the coordinate plane. Find the number of ways Bob can color five points in {(x,y)∣1≤x,y≤5} blue such that the distance between any two blue points is not an integer.
Original LaTeX notation
Bob is coloring lattice points in the coordinate plane. Find the number of ways Bob can color five points in $\{(x, y) \mid 1 \leq x, y \leq 5\}$ blue such that the distance between any two blue points is not an integer.

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