Further Analysis on the "King and Rook vs. King on a Quarter-infinite Board" Problem

Guy and Nowakowski posed the following open problem: Played on a quarter-infinite board, with initial position WKa1, WRb2 and BKc3. Can White win? Low and Stamp showed that White has a winning strategy that can be implemented within a 9×11 region. In this short note, we extend this result and show the following: With initial position WK(1, 1), WR(x, y) and BK(a, b), where 1 < x < a, White has a winning strategy that can be implemented within an (a + b + 3) × (a + b + 5) region.