#
# Lenny Conundrum Round 284
# http://www.neopets.com/games/conundrum_feature.phtml?round=284
#
# You have four numbers: 553, 546, 897, and 318. However, the numbers aren't
# what they seem. One of the numbers (I'm not telling you which!) is actually
# in base 13, one is in base 17, one is in base 19, and one is in base 23.
# It's just coincidence that all four numbers only use digits 9 and below.
#
# Now, if you add all four numbers and convert them to base 32 notation, the
# resulting number can also be written only using digits 0-9. What is that
# sum, as denoted in base 32? For example, if the sum in base 10 was 288, you
# would submit the base 32 answer: 90.
#

use strict;
use warnings;

use Algorithm::Loops qw( NextPermuteNum );
use List::Util       qw( sum );

{
    my @nums = (0..9,'a'..'z','A'..'Z');
    my %nums = map { $nums[$_] => $_ } 0..$#nums;

    sub to_base
    {
        my $base   = shift;
        my $number = shift;
        return $nums[0] if $number == 0;
        my $rep = ""; # this will be the end value.
        while( $number > 0 )
        {
            $rep = $nums[$number % $base] . $rep;
            $number = int( $number / $base );
        }
        return $rep;
    }

    sub fr_base
    {
        my $base = shift;
        my $rep  = shift;
        my $number = 0;
        for( $rep =~ /./g )
        {
            $number *= $base;
            $number += $nums{$_};
        }
        return $number;
    }
}


my @nums  = ( 553, 546, 897, 318 );
my @bases = (  13,  17,  19,  23 );

@bases = sort @bases;
do {
   my $sum32 = to_base( 32, sum( map { fr_base( $bases[$_], $nums[$_] ) } 0..$#bases ) );

   print( join( ' + ', map { "$nums[$_]($bases[$_])" } 0..$#bases ),
          " = $sum32(32)",
          ( $sum32 =~ /[^0-9]/ ? '' : '  <----' ),
          "\n"
        );
} while NextPermuteNum( @bases );


__END__
553(13) + 546(17) + 897(19) + 318(23) = 6uc(32)
553(13) + 546(17) + 897(23) + 318(19) = 7pk(32)
553(13) + 546(19) + 897(17) + 318(23) = 6na(32)
553(13) + 546(19) + 897(23) + 318(17) = 7ua(32)
553(13) + 546(23) + 897(17) + 318(19) = 726(32)  <----
553(13) + 546(23) + 897(19) + 318(17) = 7du(32)
553(17) + 546(13) + 897(19) + 318(23) = 6ug(32)
553(17) + 546(13) + 897(23) + 318(19) = 7po(32)
553(17) + 546(19) + 897(13) + 318(23) = 6bi(32)
553(17) + 546(19) + 897(23) + 318(13) = 86a(32)
553(17) + 546(23) + 897(13) + 318(19) = 6me(32)
553(17) + 546(23) + 897(19) + 318(13) = 7lu(32)
553(19) + 546(13) + 897(17) + 318(23) = 6ng(32)
553(19) + 546(13) + 897(23) + 318(17) = 7ug(32)
553(19) + 546(17) + 897(13) + 318(23) = 6bk(32)
553(19) + 546(17) + 897(23) + 318(13) = 86c(32)
553(19) + 546(23) + 897(13) + 318(17) = 6r6(32)
553(19) + 546(23) + 897(17) + 318(13) = 7eu(32)
553(23) + 546(13) + 897(17) + 318(19) = 72g(32)
553(23) + 546(13) + 897(19) + 318(17) = 7e8(32)
553(23) + 546(17) + 897(13) + 318(19) = 6mk(32)
553(23) + 546(17) + 897(19) + 318(13) = 7m4(32)
553(23) + 546(19) + 897(13) + 318(17) = 6ra(32)
553(23) + 546(19) + 897(17) + 318(13) = 7f2(32)