Here is my solution (176 chars if data is joined in a single string in $_). Do you have a test suite?

$_ = join '', @b;

s#(.)/(.)$#$1.(10-$1).$2#e;s# ?#a#g;
s#XaXaXa$#10a10a10a#;s#Xa(\da\da)$#10a$1#;
1while s#Xa(\d+)a(\d+)#10a$1a$2a$1a$2#||
s#(\d+)a/a(\d+)#"$1a".(10-$1)."a$2a$2"#e;
$s+=$_ for/\d+/g;

print "$_: $s\n";
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Aziz,,,

update:removed an extra $1 at the end of line 2 and added a missing 'a'. Score: 176 from 177

Major Update:

That code was wrong. Here is an update that works for the test cases: (score 131)

update:wrote it in sub form: score 144

print score(join'',qw(5 / 6 3 X X 7 0 4 3 X 4 / 8 1 3 / 6)),"->146\n";
print score(join'',qw(X X X X X X X X X X X X)), "->300\n";
print score(join'',qw(0 / X 0 / X 0 / X 0 / X 0 / X 0 /)),"->200\n";
print score(join'',qw(X 0 / X 0 / X 0 / X 0 / X 0 / X 0)),"->200\n";

sub score={
#        1         2         3         4         5         6
#234567890123456789012345678901234567890123456789012345678901234567890
($_,$s)=@_;1while s#(.)/(.)#$1.($1<1?'x':10-$1)."\L$2y".$2#e||s#X(\d\d
+)#x$1$1#||s#X(..)#"x\L$1z".$1#e||s#(y.|z..)$##||s#x#55#;$s+=$_ for/\d
+/g;$s
#####
}
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