Question #40323

This question tests the student's ability to rigorously handle the Greatest Integer Function (GIF) in multivariable equations.

The primary trap is the assumption that $[x+y] = [x]+[y]$ and $[x-y] = [x]-[y]$ hold universally, which would incorrectly suggest the equation is an identity valid over the entire $64 \times 64$ domain (yielding an area of 4096).

Alternatively, students might test random points and incorrectly guess a symmetry that yields half the area (2048).

The 'Golden Path' requires decomposing the variables into integer and fractional parts, revealing that the equation forces the sum of two non-negative indicator variables to be zero.

This restricts the valid domain to a specific triangular sub-region of area 1/4 within every unit square, rewarding systematic domain analysis over algebraic shortcuts.