### Re^4: Dueling Flamingos: The Story of the Fonality Christmas Golf Challenge

by eyepopslikeamosquito (Chancellor)
 on Dec 18, 2012 at 10:12 UTC ( #1009329=note: print w/replies, xml ) Need Help??

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\$IVCXL91-80\$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/IVCXL91-80/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/CLXVI60-9/MDCLXVIX/d
for \$t=~/./g; return \$s }

sub pmo2 { my \$t = shift; my \$s;
(\$s.="57e\$_"%474976)=~y/CLXVI0-9/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";

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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.

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