# [Haskell-beginners] Project Euler #01 on HackerRank, Performance issue‏

Arjun Comar nrujac at gmail.com
Thu Jan 29 01:27:22 UTC 2015

```That's why I warned about errors :).

Thanks for the catch.

On Wed, Jan 28, 2015 at 4:04 PM, Chaddaï Fouché <chaddai.fouche at gmail.com>
wrote:

> Well I did it pretty dirty, not trying to simplify my solution (I'm
> skeptic of "k * n/k = n" given that this "n / k" is really "floor (n / k)"
> ... does this really work for you ?), this gave me :
>
>
> main = do
>     replicateM_ t (readLn >>= print . pe1 . subtract 1)
>
> pe1 n = ( (3 + m3 * 3) * m3 + (5 + m5 * 5) * m5 - (15 + m15 * 15) * m15 )
> `quot` 2
>   where
>     m3 = n `quot` 3
>     m5 = n `quot` 5
>     m15 = n `quot` 15
>
>
> Note that the sum of multiples of 3/5/15 can be seen as a sum of terms of
> an arithmetic sequence which is always "number of terms * (first term +
> last term) / 2", easily proven by the expedient of writing the sequence
> twice : one in the right order and the other in reverse under it, you then
> see that the sum of two term in column is always the same so ...
>
> --
> Jedaï
>
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