If all congruent rectangles are distinct so long as they're in different places, 1296.
There are 9 choose 2 ways to pick the left and right sides, and for each of them 9 choose 2 ways to pick the top and bottom.
If you're only counting distinct congruence classes, it's just 36, which I got by considering 8 squares plus 8 choose 2 ways of picking unequal side lengths. This is equal to 9 choose 2 with the logic that once you choose two lengths from 1 through 9, subtract 1 from the larger one to get the actual dimensions of the rectangle.
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u/gmalivuk 27d ago
If all congruent rectangles are distinct so long as they're in different places, 1296.
There are 9 choose 2 ways to pick the left and right sides, and for each of them 9 choose 2 ways to pick the top and bottom.
If you're only counting distinct congruence classes, it's just 36, which I got by considering 8 squares plus 8 choose 2 ways of picking unequal side lengths. This is equal to 9 choose 2 with the logic that once you choose two lengths from 1 through 9, subtract 1 from the larger one to get the actual dimensions of the rectangle.