The following code should produce the correct output. I have tested it individually on a handful of the "expected output" numbers. I am going to let it run overnight to see how long it takes. Using

it is 44 lines of code.

`#!/usr/bin/perl
use strict;
use warnings;
use Algorithm::Loops qw/NextPermute NestedLoops/;
use Integer::Partition::Unrestricted; # see http://perlmonks.org/?node
+_id=533164
my %lookup = (
E => 0, e => 0, J => 1, j => 1, N => 1, n => 1, Q => 1, q => 1, R
+=> 2, r => 2,
W => 2, w => 2, X => 2, x => 2, D => 3, d => 3, S => 3, s => 3, Y
+=> 3, y => 3,
F => 4, f => 4, T => 4, t => 4, A => 5, a => 5, M => 5, m => 5, C
+=> 6, c => 6,
I => 6, i => 6, V => 6, v => 6, B => 7, b => 7, K => 7, k => 7, U
+=> 7, u => 7,
L => 8, l => 8, O => 8, o => 8, P => 8, p => 8, G => 9, g => 9, H
+=> 9, h => 9,
Z => 9, z => 9
);
my ($fh, $part, %data) = (undef, Integer::Partition::Unrestricted->new
+(), ());
open($fh, '<', 'dictionary.txt') or die "Unable to open 'dictionary.tx
+t' for reading: $!";
while (<$fh>) {
chomp;
my $num = join '', map {defined $lookup{$_} ? $lookup{$_} : ()} sp
+lit //, $_;
push @{$data{$num}}, $_;
}
$data{$_} = [$_] for 0 .. 9;
open($fh, '<', 'input.txt') or die "Unable to open 'input.txt' for rea
+ding: $!";
while (<$fh>) {
chomp;
my $num = $_;
$num =~ s/\D//g;
my $next = $part->gen_iter(length($num));
while (my @part = sort {$a <=> $b} $next->()) {
my $ones = "@part" =~ tr/1//;
next if $ones > ((@part - 1) / 2 + 1);
my $ok = 1;
while ($ok) {
next if "@part" =~ /\b1 1\b/;
my $template = join '', map {'A' . $_} @part;
my @dig = unpack($template, $num);
next if grep {! defined $data{$_}} @dig;
my @solution = map {[@{$data{$_}}]} @dig;
my $iter = NestedLoops( \@solution );
while (my @list = $iter->()) {
print "$_: @list\n";
}
}
continue {
$ok = NextPermute(@part);
}
}
}
`

In a nutshell, it generates the unrestricted integer partitions of the number. It skips over any partitioning that has so many 1s it could not satisfy the problem constraints. It then generates all permutations of each possible partition - skipping over partitioning with two adjacent 1s. It then checks if it produces a valid solution. I am sure it could be optimized a lot, but that would add code complexity and lines of code.

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