Consider the grid of points X = ( m, ) | 0 m, 4 . We say pair of points {(a, b), (c, d)} in X is knight- move pair if ( = 2 and = 1) or ( = 1 and = 2 ) . The number of knight-move pairs in X is:
Hint 1: Start by analyzing the initial conditions and setting up the basic equations. Consider the grid as shown.
Hint 2: Look for algebraic properties, symmetry, or geometric theorems to simplify. Each line represents the allowed move from one and point of line to other end point of line we can see the.
Hint 3: Proceed with the final algebraic steps to solve the system. movement allowed in 3 × 2, 2 × 2 rectangle, vertical or horizontal. In each rectangle there are 4 moves allowed.
Step 1: Consider the grid as shown.
Step 2: Each line represents the allowed move from one and point of line to other end point of line we can see the
Step 3: movement allowed in 3 × 2, 2 × 2 rectangle, vertical or horizontal. In each rectangle there are 4 moves allowed
Step 4: and total number of rectangle are 12.
Step 5: => Total allowed moved = 12 × 4 = 48.
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