Beat you - 24 permutations (if my Perl hash can count right.)
code:
use strict;
my %d;

&a(1,2,3,4);
print scalar (keys %d) ."\n";
foreach my $x (sort keys %d)
{
print "$x\n";
}

sub a($a,$b,$c,$d)
{
my ($a,$b,$c,$d)=@_;
my $z;
for (my $i = 1; $i <=4; $i++)
{
for (my $j = 1; $j <=6; $j++)
{
for (my $k = 1; $k <=4; $k++)
{
$d{"$a,$b,$c,$d"}=1;
$z = $b;
$b = $c;
$c = $d;
$d = $z;
}
$z = $a;
$a = $b;
$b = $z;
}
$z = $c;
$c = $d;
$d = $z;
}
}

c:\data\scripts>junk.pl
24
1,2,3,4
1,2,4,3
1,3,2,4
1,3,4,2
1,4,2,3
1,4,3,2
2,1,3,4
2,1,4,3
2,3,1,4
2,3,4,1
2,4,1,3
2,4,3,1
3,1,2,4
3,1,4,2
3,2,1,4
3,2,4,1
3,4,1,2
3,4,2,1
4,1,2,3
4,1,3,2
4,2,1,3
4,2,3,1
4,3,1,2
4,3,2,1

code:
function game24($a,$b,$c,$d)

Dim $h, $j, $l, $p, $q, $r, $s, $t, $v, $, $x, $y, $z
$h = "+","-","/","*"
for $z=1 to 4
for $y=1 to 6
for $x=1 to 4
for each $p in $h
for each $q in $h
for each $r in $h
for each $j in split("0,8~0,8,10,18~0,12~4,16","~")
$ = ".0"
$s = ""+$a+$+$p+$b+$+$q+$c+$+$r+$d+$
for each $ in split($j,",")
$l = chr(40 + ($l="("))
$s = "" + left($s,$) + $l + substr($s,1+$)
next
$t = execute("$$v=$s")
if abs($v-24)< 1E-9
goto E
endif
next
next
next
next
$ = $b
$b = $c
$c = $d
$d = $
next
$ = $a
$a = $b
$b = $
next
$ = $c
$c = $d
$d = $
next
$s = ""

:E
$game24 = $s
exit
endfunction



[ 24. September 2002, 02:53: Message edited by: Howard Bullock ]
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