in reply to How to determine & record all possible variations for 5 items?

In the spirit of TIMTOLanguageTDI, here's a way to do it in Haskell:

Note that this will take a while, as there are over 4.5 million solutions. This doesn't take into account the "only multiples of 2 or 5" criteria, but it's easy to change it so that it does:partition :: Integer -> Integer -> [[Integer]] partition total 1 = [[total]] partition total numparts = concat $ map (prepend) [total, (total - 1) .. 0] where prepend x = map (x:) (subpart x) subpart x = partition (total - x) (numparts - 1) -- then: partition 100 5

And this gives about 600k solutions. Much more manageable.partition :: Integer -> Integer -> [[Integer]] partition total 1 = [[total]] partition total numparts = concat $ map (prepend) numlist where prepend x = map (x:) (subpart x) subpart x = partition (total - x) (numparts - 1) numlist = filter twoorfive [total, (total - 1) .. 0] twoorfive x = x `mod` 2 == 0 || x `mod` 5 == 0

Another way to do it would be to create all possible lists of the desired length (5 in this case), with each element in a given range (0..100 here) and filter out the ones that don't sum to 100. I tried this approach as a mind exercise (you probably wouldn't want to use it because it would be very ineffecient). I got it to work, but only by hardcoding the number of elements to five, using a list comprehension. I know this is a Perl board, but anyone familiar with Haskell know of an easy and intuitive way to do something like:

AndallLists :: Integer -> Integer -> [[Integer]] allLists n len = ?

`allLists`would return all lists of length

`len`where each element is in the range

`0..n`?

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