2 A puzzle involves a 3 by 3 grid of squares, numbered 1 to 9, as shown in Fig. 1a below. Eight of the squares are covered by blank tiles. Fig. 1b shows the puzzle with all of the squares covered except for square 4 . This arrangement of tiles will be called position 4. \begin{table}[h]

1. Apply the algorithm with the inputs \(B = 2\) and \(N = 5\). Record the values of \(F , G , H , C\) and \(N\) each time Step 9 is reached.
2. Explain what happens when the algorithm is applied with the inputs \(B = 2\) and \(N = - 5\).
3. Apply the algorithm with the inputs \(B = 10\) and \(N = 37\). Record the values of \(F , G , H , C\) and \(N\) each time Step 9 is reached. What are the output values when \(B = 10\) and \(N\) is any positive integer?