Project Euler 1

I took a look at the first problem on the Project Euler site earlier this afternoon:

This asks you to find the sum of the natural numbers that are less than 1000 and are multiples of 3 or 5.

I decided that Haskell’s filter function and a lambda would make this problem trivially easy to solve. In GHCi:

Prelude> let sumMultiplesOf3Or5 max = sum(filter(\x -> (mod x 3 == 0) || (mod x 5 == 0))[1 .. max - 1])
Prelude> sumMultiplesOf3Or5 1000

As I played around with other values for max, something unexpected appeared before my eyes. A pattern of repeated digits begins to emerge in the sums of the multiples of 3 and 5 less than 10 to the power of i as i increases.

Prelude> map sumMultiplesOf3Or5 (map (\i -> 10 ^ i) [1..6])

Something similar happens with the sums of the multiples of 3 or 5 less than 20, 200,…,30,300, and so on:

Prelude> map (\j -> map sumMultiplesOf3Or5 (map (\i -> j * 10 ^ i) [1..6])) [1..9]


[[23,2318,233168,23331668,2333316668,233333166668], -- [10,100,1000,10000,100000,1000000]
[78,9168,931668,93316668,9333166668,933331666668], -- [20,200,2000,20000,200000,2000000]
[195,20850,2098500,209985000,20999850000,2099998500000], -- and so on

I’m not sure if this continues indefinitely. I wonder if similar patterns emerge with numbers in different bases. I’m curious about trying multiples of numbers other than 3 or 5. At this point, I’ve really no idea why this happens, but my curiosity is aroused.

I’m also really impressed with Haskell, a language that I barely know. The only other time I’ve used functional programming seriously is with C# and VB.Net for LINQ, of which I am a huge fan.

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