puri
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 Sep24 awarded Autobiographer Feb27 awarded Notable Question Dec23 awarded Nice Answer Jun24 revised How do we show the equality of these two summations? edited body Sep17 awarded Commentator Sep17 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language I feel the same for Napoleon's theorem en.wikipedia.org/wiki/Napoleon%27s_Theorem Apr19 awarded Popular Question Feb27 awarded Yearling Feb18 awarded Nice Answer Nov1 answered How do we show the equality of these two summations? Feb2 awarded Nice Question Nov2 accepted Number of ways to partition a rectangle into n sub-rectangles Nov2 comment Number of ways to partition a rectangle into n sub-rectangles 1, 2, 6, 15 are exactly the numbers I have when I count by hands (including all rotations and reflections.) I will appreciate if you can share the recurrence relation or point me to a publication. Aug8 comment Number of ways to partition a rectangle into n sub-rectangles Interesting but I wonder if your graph representation will be sufficient. From the second example above, sliding the partitions the other way around from "clockwise" to "counter-clockwise" will result in another way to partition with the exactly same graph. Aug5 comment Number of ways to partition a rectangle into n sub-rectangles @Jens It doesn't matter where exactly the lines are. What matters is the overall form. Aug4 awarded Teacher Jul30 comment Watchdog Problem I indeed forgot. Thanks. Jul30 revised Watchdog Problem added 9 characters in body; edited tags; added 2 characters in body Jul30 comment Number of ways to partition a rectangle into n sub-rectangles No, I don't take length into accounts. Frankly I don't know how to rephrase the question to be more mathematically specific. This question is tagged "computer-science" because I am thinking of generating all of these patterns and objectively choosing the "best-looking" ones, and it would be nice to be able to take a look at all of them. If there is a solution, it's good. If not, I want to be sure that it is still a open problem. Then how about good approximation or related problems? Jul29 awarded Scholar