#!perl

use strict;
use warnings FATAL => 'uninitialized';

use lib 'lib';

#  In response to mjd's comments on his blog post at
#
#    http://blog.plover.com/math/17-puzzle.html
#
#  I present my solution to the problem. Most entertaining.
#
#  T. Alex Beamish / August 11, 2016

use Permute;

{
    my @values = ( 6, 6, 5, 2 );
    my @ops = qw/+ - \/ */;

    my $possibilities = Permute::possibilities( \@values );

    foreach my $v ( @{$possibilities} ) {

      for my $o1 ( @ops ) {
        for my $o2 ( @ops ) {
          for my $o3 ( @ops ) {

            my @list = ( $v->[0], $o1, $v->[1], $o2,
                         $v->[2], $o3, $v->[3] );

            #  Just try the expression as-is, without any brackets.

            display ( \@list );

            #  Now we're going to insert a pair of brackets into the
            #  expression, making sure that a) they encompass at least
            #  a number, an operation, and another number, and b) we
            #  don't bother by bracketing the entire expression, as
            #  that's redundant.

            for my $lb ( 0, 2, 4 ) {
              for my $rb ( 4, 6, 8 ) {

                next unless ( $lb + 2 < $rb );          #  a)
                next if ( $lb == 0 && $rb == 8 );       #  b)

                my @blist = @list;
                splice ( @blist, $lb, 0, '(', @blist[ $lb .. -1 ] );
                splice ( @blist, $rb, 0, ')', @blist[ $rb .. -1 ] );

                display ( \@blist );
              }
            }
          }
        }
      }
    }
}

#  Since we have a duplicated value, we can add a hash to catch
#  expressions identical to the ones we've evaluated already.
#  It won't catch the similarity between '2*5' and '5*2' that
#  evaluate to the same value. Oh well.

my %tried_that;

sub display {

    my ( $list ) = @_;

    my $expression = join('',@{$list});
    if ( exists $tried_that{ $expression } ) { return; }
    $tried_that{ $expression } = 1;

    my $result = eval $expression;
    if ( defined $result ) {

      print "$expression = $result\n";

    } else {

      print "$expression is undefined.\n";
    }
}