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How many rectangles are there in the puzzle?

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But there is a shortcut that greatly simplifies the problem. The key insight is that any two horizontal lines combined with any two vertical lines will form a rectangle. So the question reduces to: how many ways are there to pick 2 horizontal lines and 2 vertical lines? read more

There are 200 small rectangles. All that remains is to figure out how many rectangles can be found in a 10*10 square. From now on I will ignore the small rectangles and just refer to small squares (made of 2 small rectangles each). Imagine writing down in each square the number of rectangles that can be made with that square as their top left corner. read more

There are 6 1x4 rectangles. There are 20 2x1 rectangles. There are 15 2x2 rectangles. There are 10 2x3 rectangles. There are 5 2x4 rectangles. There are 16 3x1 rectangles. There are 12 3x2 rectangles. There are 8 3x3 rectangles. There are 4 3x4 rectangles. There are 12 4x1 rectangles. There are 9 4x2 rectangles. There are 6 4x3 rectangles. There are 3 4x4 rectangles. There are 8 5x1 rectangles. read more

My year 10 class think that the puzzle is quite clever because it fools you into a quick answer, but then you start see the puzzle in a bit more depth and more rectangles appear. We think the answer is 26, but are not 100% sure. read more

There are 200 small rectangles. All that remains is to figure out how many rectangles can be found in a 10*10 square. From now on I will ignore the small rectangles and just refer to small squares (made of 2 small rectangles each). read more

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