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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

Consider the grid of points X=\ (m, n) 0 ≤ m, n ≤ 4\ . We say a...

Consider the grid of points X={(m,n)∣0≤m,n≤4}X=\{(m, n) \mid 0 \leq m, n \leq 4\}. We say a pair of points {(a,b),(c,d)}\{(a, b),(c, d)\} in XX is a knightmove pair if (c=a±2(c=a \pm 2 and d=b±1)d=b \pm 1) or (c=a±1(c=a \pm 1 and d=b±2)d=b \pm 2). The number of knight-move pairs in XX is:Consider the grid of points X=\ (m, n) 0 ≤ m, n ≤ 4\ . We say a pair of points \ (a, b),(c, d)\ in X is a knightmove

Correct answer

48

Step-by-step solution

Consider the grid of points X=\ (m, n) 0 ≤ m, n ≤ 4\ . We say a pair of points \ (a, b),(c, d)\ in X is a knightmove
Consider the grid as shown. Each line represents the allowed move from one and point of line to other end point of line we can see the movement allowed in 3×2,2×23 \times 2,2 \times 2 rectangle, vertical or horizontal. In each rectangle there are 4 moves allowed and total number of rectangle are 12 . ∴\therefore Total allowed moved =12×4=48=12 \times 4=48.
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