Problem Statement

Find the largest base 10 integer whose digits are all different,   and   is evenly divisible by each of its individual digits.

These numbers are also known as   Lynch-Bell numbers,   numbers   n   such that the (base ten) digits are all different (and do not include zero)   and   n   is divisible by each of its individual digits.

135   is evenly divisible by   1,   3,   and   5.

Note that the digit zero (0) can not be in the number as integer division by zero is undefined. The digits must all be unique so a base ten number will have at most 9 digits. Feel free to use analytics and clever algorithms to reduce the search space your example needs to visit, but it must do an actual search. (Don't just feed it the answer and verify it is correct.)

Do the same thing for hexadecimal.

Let's start with the solution:

USING: io kernel math math.combinatorics math.parser math.ranges
sequences tools.time ;
IN: rosetta-code.largest-divisible

: all-div? ( seq -- ? )
    [ string>number ] [ string>digits ] bi [ mod ] with map
    sum 0 = ;

: n-digit-all-div ( n -- seq )
    "12346789" swap <combinations>
    [ [ all-div? ] filter-permutations ] map concat ;

: largest-divisible ( -- str )
    8 [ dup n-digit-all-div dup empty? ] [ drop 1 - ] while 
    nip supremum ;

: largest-divisible-demo ( -- )
    [ largest-divisible print ] time ;

MAIN: largest-divisible-demo