in reply to Re^3: Dueling Flamingos: The Story of the Fonality Christmas Golf Challenge in thread Dueling Flamingos: The Story of the Fonality Christmas Golf Challenge
As an aside, there are no other solutions of the form that Ton used (1x$&*XX where Ton's XX is 40).
It seems that his solution truly is a one of a kind!
In addition to the one used in the 2006 Fonality golf challenge:
s!.!y$IVCXL426(:$XLMCDIVX$dfor$$_.=5x$&*8%29628
don't forget about Ton's original one
of equal length:
s!.!y$IVCXL9180$XLMCDXVIII$dfor$$_.=4x$&%1859^7
used in the 2004 Polish golf tournament.
Update: Here is a test program to verify that all four magic formulae are correct:
use strict;
use Roman;
sub ton1 { my $t = shift; my $s;
($s.=4x$_%1859^7)=~y/IVCXL9180/XLMCDXVIII/d
for $t=~/./g; return $s }
sub ton2 { my $t = shift; my $s;
($s.=5x$_*8%29628)=~y/IVCXL426(:/XLMCDIVX/d
for $t=~/./g; return $s }
sub pmo1 { my $t = shift; my $s;
($s.="32e$_"%72726)=~y/CLXVI609/MDCLXVIX/d
for $t=~/./g; return $s }
sub pmo2 { my $t = shift; my $s;
($s.="57e$_"%474976)=~y/CLXVI09/MDCLXIXV/d
for $t=~/./g; return $s }
for my $i (1..3999) {
my $r = uc roman($i);
my $t1 = ton1($i);
my $t2 = ton2($i);
my $p1 = pmo1($i);
my $p2 = pmo2($i);
print "$i: $r\n";
$r eq $t1 or die "t1: expected '$r' got '$t1'\n";
$r eq $t2 or die "t2: expected '$r' got '$t2'\n";
$r eq $p1 or die "p1: expected '$r' got '$p1'\n";
$r eq $p2 or die "p2: expected '$r' got '$p2'\n";
}
print "all tests successful\n";
Re^5: Dueling Flamingos: The Story of the Fonality Christmas Golf Challenge by primo (Beadle) on Dec 18, 2012 at 11:15 UTC 
I tried many magic formulas, but this happens to be one of the first
ones I tried since the $m x $& tends to multiply the result by 10 each
time, so getting a result that's one longer each time, about the only
somewhat regular pattern in roman numerals.
 Ton, remarking on how he found his magic formula back in 2004
I suppose if I had done my research better, I would have known that Ton had reached his result based on exactly the same methodology that I posted above. But seriously:
4x$&%1859^7
xor 7? Now that's just crazy.
 [reply] [d/l] 
