<p>Find the total number of rectangles on the normal chessboard.</p>
Step-by-Step Solution
Key Concept: A rectangle on a chessboard is uniquely determined by choosing 2 horizontal lines from 9 available and 2 vertical lines from 9 available. This is because an 8×8 chessboard has 9 horizontal and 9 vertical lines forming the grid.
<p><strong>Step 1:</strong> Understand the grid structure. A standard 8×8 chessboard is formed by 9 horizontal lines and 9 vertical lines (including borders).</p><p><strong>Step 2:</strong> To form a rectangle, we need to select exactly 2 horizontal lines from 9 available lines and exactly 2 vertical lines from 9 available lines.</p><p><strong>Step 3:</strong> Number of ways to choose 2 horizontal lines = C(9,2) = 9×8/2 = 36</p><p><strong>Step 4:</strong> Number of ways to choose 2 vertical lines = C(9,2) = 9×8/2 = 36</p><p><strong>Step 5:</strong> Total number of rectangles = C(9,2) × C(9,2) = 36 × 36 = 1296</p><p>∴ Answer: <strong>1296</strong></p>
Correct Answer: 1296