[Haskell-cafe] complex multiplication function in Haskell

[Richard A. O'Keefe]

> On 27/04/2017, at 12:02 AM, Mahmoud Murad <mahmoudmurad92 at gmail.com> wrote:
> 
> Hi there, 
> The number 354162 has 6 digits and contains all digits from 1 to 6, and it can be considered as a multiplication of 3 * 54 = 162.  
> so what I need is a function that will take all the real number and return the number that can be split as above,  
> 354162  .. 3 * 54 = 162   
> I have no idea how to do such a thing! any help! 

Start by spelling out just what the conditions are.
- Are you looking specifically for 6-digit numbers or could it be more?
  (Because you say "ALL the real number[s]".
- Are you sure you want REAL numbers and not INTEGERS?

One way to read what you have written is
 - find a permutation [a,b,c,d,e,f] of [1,2,3,4,5,6]
 - such that a*(b*10+c) == (d*10+e)*10+f.
There are only 6! = 720 permutations of six digits,
so not a lot to check.  For a computer program, I'd just
code that.
We can restructure this as
- find three different digits 1 <= a,b,c <= 6
- compute def = a*(b*10+c)
- check that the digits of def are all 1..6 and all
  different and different from a,b,c.
There are 120 cases to check here.

As it happens, Data.List provides permutations
Prelude> import Data.List
Prelude Data.List> permutations [1..3]
[[1,2,3],[2,1,3],[3,2,1],[2,3,1],[3,1,2],[1,3,2]]
Prelude Data.List> length (permutations [1..6])
720

You can combine this with a list comprehension to get the numbers
you want.