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Considering the absolute value of the difference in velocities. That is the relative velocity.
Asking for a square of area A is the same thing than asking for a square of diagonal sqrt(2 * a) (check it). The diagonal of the inner square as a function of time is d = L * sqrt(2) - rel_vel * time. We have then a linear equation instead of a quadratic one
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Sherlock and Moving Tiles
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You can simplify the problem by:
Considering the absolute value of the difference in velocities. That is the relative velocity.
Asking for a square of area A is the same thing than asking for a square of diagonal sqrt(2 * a) (check it). The diagonal of the inner square as a function of time is d = L * sqrt(2) - rel_vel * time. We have then a linear equation instead of a quadratic one