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| Math Central | Quandaries & Queries |
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Question from Brian: Looking for a formula where I can type in a number, 17 for example, and using the numbers 1 through 17 (1, 2, 3, 4 etc....), to come up with all possible combinations, when added, that will equal 17. And each number can only be used once. I've tried a few search engines but my computer stares at me blankly and scratches its head :-/. |
Brian,
Your project is called “partitions into distinct parts” (or sometimes “strict partitions”). They are quite interesting — see what Wikipedia has to say:
https://en.wikipedia.org/wiki/Partition_(number_theory)#Odd_parts_and_distinct_parts
You can find a fairly long list in the on-line encyclopedia of integer sequences (oeis.org). Just type in 1,1,2,2,3,4,5,6,8
Chris
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