Take the number 192 and multiply it by each of 1, 2, and 3:

192 × 1 = 192
192 × 2 = 384
192 × 3 = 576

By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)

The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).

What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n > 1?



In [7]:

    
let panOneNine = string(123456789)

let isOneNinePandigital n =     
    let n_sorted = new string (string(n).ToCharArray() |> Array.sort)
    if n_sorted.Length > 9 then false
    else n_sorted = panOneNine
    
let isPandigitalConcatProduct (x,n) = 
    let number = 
        [1..n]
        |> List.map (fun i -> string(x * i))
        |> String.concat ""
        
    if (isOneNinePandigital number) then int(number) 
    else 0
   
let pairWith lst x = 
    lst |> List.map (fun element -> (x,element))
    
[1..10000]
|> List.map (pairWith [1..50])
|> List.concat
|> List.map isPandigitalConcatProduct
|> List.filter (fun x -> x <> 0)
|> List.sortDescending
|> List.head









    Out[7]:





932718654