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Re: Puzzle: What is the largest integer whose digits are all different (and do not include 0) that is divisible by each of its individual digits?

by barrachois (Pilgrim)
 on Oct 28, 2005 at 19:47 UTC ( #503751=note: print w/replies, xml ) Need Help??

Many good replies above, but figured I'd try it for myself with the help of CPAN. Looks like it runs plenty fast enough with brute force alone. Fun.
```#!/usr/bin/perl -w
#
# See http://perlmonks.org/?node_id=503317, Oct 27 2005
# Jim Mahoney (mahoney@marlboro.edu)
#
use strict;
use warnings;
use Algorithm::FastPermute qw(permute);
use Math::Combinatorics qw();

my \$debug = 0;
my \$largest = 0;
my @solutions;
my \$start_time = time();

print "
What is the largest integer whose digits are all different
(and do not include 0) that is divisible by each of its individual di
+gits?
Working...
";

for my \$n (reverse 1..9){
my \$c = Math::Combinatorics->new( count=>\$n, data=>[1..9] );
while (my @array = \$c->next_combination){
permute { remember(@array) if is_solution(@array) } @array;
}
}
@solutions = sort @solutions;

print "
Done in " . (time()-\$start_time) . " seconds.
Total number of solutions found is " . scalar(@solutions) . ".
Largest is " . \$solutions[-1] . ".
";

sub remember {
my @digits = @_;
push @solutions, join('',@digits);
}

sub is_solution {
my @digits = @_;
my \$number = 0+join('',@digits);
for my \$digit (@digits){
return 0 if \$number % \$digit != 0;
}
return 1;
}

__END__

\$ ./n_digits_divide.pl

What is the largest integer whose digits are all different
(and do not include 0) that is divisible by each of its individual di
+gits?
Working...

Done in 6 seconds.
Total number of solutions found = 548.
Largest found was 9867312.

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