..........   0000000000
.......c..   0000000200
.lauze.o..   0211110100
.e.....a..   0100000100
.g.....r..   0200000100
baronies..   1533553100
.t.....e..   0200000100
.e.....r..   0100000200
..........   0000000000
..........   0000000000

##</code><code>##

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11108138
use warnings;
use Path::Tiny;
use List::Util qw( shuffle uniq first );
$SIG{__WARN__} = sub { die @_ };

my $n = 10;
my $maxtiles = 7;
my $upwords = 1; # 0 => extending(normal scrabble?)  1 => upwords

my $n1 = $n + 1;
my $board = ('.' x $n . "\n") x $n;
my $heights = $board =~ tr/./0/r;
my @dictwords;
my $filename = "words.11108138.$n"; # for caching
if( -f $filename )
  {
  @dictwords = split /\n/, path($filename)->slurp;
  }
else
  {
  @dictwords = sort { length $b <=> length $a }
    grep /^[a-z]{2,$n}$/,
    path('/usr/share/dict/words')->lines({chomp => 1});
  path($filename)->spew(map "$_\n", @dictwords);
  }

my @drawpile = shuffle + #  thanks to GrandFather 11108145
  ('a') x 9, ('b') x 2, ('c') x 2, ('d') x 4, ('e') x 12, ('f') x 2,
  ('g') x 4, ('h') x 2, ('i') x 9, ('j') x 1, ('k') x 1, ('l') x 4, ('m') x 2,
  ('n') x 6, ('o') x 8, ('p') x 2, ('q') x 1, ('r') x 6, ('s') x 4, ('t') x 6,
  ('u') x 4, ('v') x 2, ('w') x 2, ('x') x 1, ('y') x 2, ('z') x 1 ;
my @tiles = sort splice @drawpile, 0, $maxtiles;
print "tiles: @tiles\n";
my $pat = join '', map "$_?", @tiles;

my $word = first
  { /^[@tiles]+$/ and (join '', sort split //) =~ /^$pat$/ } @dictwords;
substr $board, $n1 * ($n >> 1) + ($n - length($word) >> 1),
  length $word, $word;
substr $heights, $n1 * ($n >> 1) + ($n - length($word) >> 1),
  length $word, ($upwords ? 1 : 5) x length $word;
my @chosen = $word;
my $changed = 1;
my $moves = 0;
my $b = $board =~ tr/\n/-/r;
$b =~ s/-/   $_/ for $heights =~ /.*\n/g;
print $b;

while( @tiles )
  {
  $upwords or $board =~ /\./ or last;
  $upwords && $heights =~ tr/0-4// == 0 and last;
  my @best; # [ flip, pos, pat, word ]
  my @all = (@tiles, ' ', sort +uniq $board =~ /\w/g);
  $moves++;
  print "moves: $moves  tiles: @tiles\n";
  my @subdict = grep /^[@all]+$/, @dictwords;
  for my $flip ( 0, 1 )
    {
    my $inorder = join '', map "$_?", sort "@all" =~ /\w/g;
    my $orderpat = qr/^$inorder$/;

    my @pat;
    $board =~ /(?<!\w).{2,}(?!\w)(?{
      push @pat, [ $flip, $-[0], $& ]
      })(*FAIL)/;
    $upwords and @pat = map expand($_), @pat;
    @pat = grep $_->[2] =~ /\w/, @pat;
    $upwords or
      @pat = grep { substr( $board, $_->[1], length $_->[2]) =~ /\./ } @pat;

    for my $p ( @pat )
      {
      my ($flip, $pos, $pat) = @$p;
      my @under = substr( $board, $pos, length $pat) =~ /\w/g;
      my $w = first { /^[@under@tiles]+$/
        && /^$pat$/
        && (join '', sort /\w/g ) =~ /$orderpat/
        && ( /s$/ ? $pat ne s/s$/./r : 1 )
        && ( $upwords ? matchrule( $pos, $_ ) : 1 )
        } @subdict;
      $w and $best[ length $w ] //= [ $flip, $pos, $pat, $w ];
      }
    transpose();
    }
  if( $changed = @best )
    {
    my ($flip, $pos, $pat, $word) = @{ $best[-1] };
    $flip and transpose();
    if( $upwords )
      {
      my $same = $word ^ substr $board, $pos, length $word;
      my $tmppos = $pos;
      substr( $heights, $tmppos++, 1 ) += $_ ne "\0" for split //, $same;
      }
    else
      {
      substr($heights, $pos, length $word) =~ tr/0/5/;
      }
    substr $board, $pos, length $word, $word;
    print '-' x 20, "chosen: $flip $pos $word\n";
    push @chosen, $word;
    $flip and transpose();
    my $tmpword = $word;
    $tmpword =~ s/$_// for $pat =~ /\w/g;
    my $tiles = join '', @tiles;
    $tiles =~ s/$_// for split //, $tmpword;
    @tiles = split //, $tiles;
    }
  else
    {
    splice @tiles, rand @tiles, 1; # discard random tile
    }
  @tiles = sort @tiles, splice @drawpile, 0, $maxtiles - @tiles;
  if( $changed )
    {
    my $b = $board =~ tr/\n/-/r;
    $b =~ s/-/   $_/ for $heights =~ /.*\n/g;
    print $b;
    }
  }
print "\nchosen words: @chosen\n";

sub matchrule
  {
  my ($pos, $word) = @_;
  my $tiles = join '', @tiles;
  my $bd = substr $board, $pos, length $word;
  my $count = substr $heights, $pos, length $word;
  $bd eq $word and return 0;
  for ( reverse split //, $word )
    {
    my $bchar = chop $bd;
    my $stack = chop $count;
    $_ eq $bchar and next;
    $stack >= 5 and return 0;
    $tiles =~ s/$_// or return 0;
    }
  return 1;
  }

sub transpose
  {
  local $_ = $board;
  $board = '';
  $board .= "\n" while s/^./ $board .= $& ; '' /gem;
  local $_ = $heights;
  $heights = '';
  $heights .= "\n" while s/^./ $heights .= $& ; '' /gem;
  }

sub expand
  {
  my @ans;
  my ($flip, $pos, $pat) = @{ shift() };
  push @ans, [ $flip, $pos, $` =~ tr//./cr . $& . $' =~ tr//./cr ]
    while $pat =~ /\w/g;
  return @ans;
  }

##</code><code>##

moves: 9  tiles: c g j l n q x
--------------------chosen: 1 78 coarsen
..........   0000000000
.......c..   0000000200
.gauze.o..   0111110100
.e.....a..   0100000100
.l.....r..   0100000100
baronies..   1533553100
.d.....e..   0100000100
.......n..   0000000100
..........   0000000000
..........   0000000000
moves: 10  tiles: g j l q r t x
--------------------chosen: 1 78 coarser
..........   0000000000
.......c..   0000000200
.gauze.o..   0111110100
.e.....a..   0100000100
.l.....r..   0100000100
baronies..   1533553100
.d.....e..   0100000100
.......r..   0000000200
..........   0000000000
..........   0000000000
moves: 11  tiles: e g j l q t x
--------------------chosen: 1 13 legate
..........   0000000000
.......c..   0000000200
.lauze.o..   0211110100
.e.....a..   0100000100
.g.....r..   0200000100
baronies..   1533553100
.t.....e..   0200000100
.e.....r..   0100000200
..........   0000000000
..........   0000000000