1
Question
How many different rectangles can be drawn on an 8*8 chess board?
How many different rectangles can be drawn on an 8*8 chess board?
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Solution
A square is a special type of rectangle, so we won't have to count the squares separately.
A rectangle is formed by two horizontal lines and 2 vertical lines. How many ways can you choose two vertical lines? Well there are 9 total. So 9c2. Order doesn't matter, which is why we use combinations . This equals 36.
How many ways can you choose two horizontal lines. There are 9C2. Again order doesn't matter, so we use combinations. It equals 36 again.
36 * 36 = 1296
A square is a special type of rectangle, so we won't have to count the squares separately.
A rectangle is formed by two horizontal lines and 2 vertical lines. How many ways can you choose two vertical lines? Well there are 9 total. So 9c2. Order doesn't matter, which is why we use combinations . This equals 36.
How many ways can you choose two horizontal lines. There are 9C2. Again order doesn't matter, so we use combinations. It equals 36 again.
36 * 36 = 1296
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