Thinking about the 8-queens problems, I remember a smart Perl script using a regex to solve sudoku.
For my fisrt try, I used a simple string 12345678 (8 times/lines) but I failed because I used (?<!pattern) with \digit : "A zero-width negative look-behind assertion. (...) Works only for fixed-width look-behind." (perlvar)
Finally, with a more complex string I found a solution.
The idea is a probably similar to The N-queens problem using pure regexes by Abigail-II.
Perhaps in a more golfic-way (I was a Perl Golf fan) with heavy usage of capturing ( $1 to $64 for an 8x8 chess ;-)
Here is the code : 
#!/usr/bin/perl
use strict;
use warnings;
my $n =($ARGV[0] || 8);
# usage : perl queens.pl n
# ex : perl queens.pl 20
#############
my $p=1;
my (@s,@r);
my $str;
my $re='_(\d+)!';
for my $i (1..$n) {
    for my $j (1..$n) {
        $str.= join '!',"_$j",(map {join';',$j-$_<0?0:$j-$_,$j+$_ >$n?
+0:$j+$_} (1..($n-$i))),'';
    }
    $str.="\n";
    push @s,$p+1,$p+2;
    push @r,$p;
    $re.=($i==$n)?'':(('(\d+);(\d+)!'x($n-$i)).".*?\n.*?_(?!(?:\\".(jo
+in '|\\',@r,@s).')!)(\d+)!');
    $p+=2*($n-$i)+1;
    $_+=2 for @s;
}
my $l="a";
if ($str=~$re){print join",",map{$l++.eval"\$$_"}@r} else {print "no s
+olution"}
#print "\n\n",$str;
#print "\n\n",$re;

[download]
The problem : this solver find only one solution.
Is it possible to be exhaustive ? Perhaps using s/// and modifications in the string instead of m// ?...
Below, some explanations : 
String (5x5 chess):
_1!0;2!0;3!0;4!0;5!_2!1;3!0;4!0;5!0;0!_3!2;4!1;5!0;0!0;0!_4!3;5!2;0!1;
+0!0;0!_5!4;0!3;0!2;0!1;0!
_1!0;2!0;3!0;4!_2!1;3!0;4!0;5!_3!2;4!1;5!0;0!_4!3;5!2;0!1;0!_5!4;0!3;0
+!2;0!
_1!0;2!0;3!_2!1;3!0;4!_3!2;4!1;5!_4!3;5!2;0!_5!4;0!3;0!
_1!0;2!_2!1;3!_3!2;4!_4!3;5!_5!4;0!
_1!_2!_3!_4!_5!

Regex:
_(\d+)!(\d+);(\d+)!(\d+);(\d+)!(\d+);(\d+)!(\d+);(\d+)!.*?
.*?_(?!(?:\1|\2|\3)!)(\d+)!(\d+);(\d+)!(\d+);(\d+)!(\d+);(\d+)!.*?
.*?_(?!(?:\1|\10|\4|\5|\11|\12)!)(\d+)!(\d+);(\d+)!(\d+);(\d+)!.*?
.*?_(?!(?:\1|\10|\17|\6|\7|\13|\14|\18|\19)!)(\d+)!(\d+);(\d+)!.*?
.*?_(?!(?:\1|\10|\17|\22|\8|\9|\15|\16|\20|\21|\23|\24)!)(\d+)!

Solution in : $1 $10 $17 $22 $25

_3!2;4!1;5! means :
if in this line, the queen is in column "3" (_3!),
then in next line queen will not be on column "2" or "4" (!2;4!)
and in the line after queen will not be in col "1" or "5" (!1;5!) (dia
+gonal)

[download]

In reply to N-Queens problem with a regex (again) by brx

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