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?

This looks like fun, so I've had a go :)

#!/usr/bin/perl -w
use strict;

my $biggest_number = 987654321;

BIGNUMBER: while ($biggest_number) {

    # Discard all odd numbers (not divisible by 2)
    if ($biggest_number % 2) { $biggest_number--; next BIGNUMBER; }

    my @divisors = split //, $biggest_number;

    # Discard all numbers containing zero
    if (grep {$_ eq "0"} @divisors) { $biggest_number--; next BIGNUMBE
+R; }

    # Discard all numbers with repeated digits
    my %seen = ();
    for (@divisors) {
        if ($seen{$_}++) {
            $biggest_number--; next BIGNUMBER;
        }
    }

    # Get this far, give it a try
    print "Trying $biggest_number...";
    DIVISORS:
    for (@divisors) {
        if ($biggest_number % $_) {
            $biggest_number--;
            print "Failed!\n";
            next BIGNUMBER;
        }
    }
    print "Success!!\n";
    for (@divisors) {
        print "$biggest_number / $_ = ", $biggest_number / $_, "\n";
    }
    exit;
}
[download]

Update:Well, I'd now like to stake my claim as having come up with the slowest solution that gets the correct answer, and here is my evidence:

Trying 9867312...Success!!
9867312 / 9 = 1096368
9867312 / 8 = 1233414
9867312 / 6 = 1644552
9867312 / 7 = 1409616
9867312 / 3 = 3289104
9867312 / 1 = 9867312
9867312 / 2 = 4933656

real    384m53.120s
user    382m59.960s
sys     0m14.600s
[download]

Almost 6.5 hours, I imagine that would have been quite impressive in the late 50's :D

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