29 lines
1.2 KiB
Haskell
29 lines
1.2 KiB
Haskell
-- The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it
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-- also has a rather interesting sub-string divisibility property.
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--
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-- Let d[1] be the 1st digit, d[2] be the 2nd digit, and so on. In this way, we note the following:
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--
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-- d[2]d[3]d[4]=406 is divisible by 2
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-- d[3]d[4]d[5]=063 is divisible by 3
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-- d[4]d[5]d[6]=635 is divisible by 5
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-- d[5]d[6]d[7]=357 is divisible by 7
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-- d[6]d[7]d[8]=572 is divisible by 11
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-- d[7]d[8]d[9]=728 is divisible by 13
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-- d[8]d[9]d[10]=289 is divisible by 17
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--
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-- Find the sum of all 0 to 9 pandigital numbers with this property.
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import Euler
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main = print $ sum $ do
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digits <- permutations [0..9]
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guard $ (digits!!0) /= 0
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guard $ (fromDigits $ map (digits!!) [7,8,9]) `mod` 17 == 0
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guard $ (fromDigits $ map (digits!!) [6,7,8]) `mod` 13 == 0
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guard $ (fromDigits $ map (digits!!) [5,6,7]) `mod` 11 == 0
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guard $ (fromDigits $ map (digits!!) [4,5,6]) `mod` 7 == 0
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guard $ (fromDigits $ map (digits!!) [3,4,5]) `mod` 5 == 0
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guard $ (fromDigits $ map (digits!!) [2,3,4]) `mod` 3 == 0
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guard $ (fromDigits $ map (digits!!) [1,2,3]) `mod` 2 == 0
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return (fromDigits digits)
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