note eyepopslikeamosquito <P> <blockquote> <I> 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! </I> </blockquote> In addition to the one used in the 2006 Fonality golf challenge: <CODE> s!.!y\$IVCXL426(-:\$XLMCDIVX\$dfor\$\$_.=5x\$&*8%29628 </CODE> don't forget about Ton's <a href="http://groups.google.com/group/pl.comp.lang.perl/browse_frm/thread/6e0afdfe37ec51be/dbf17d1a9c9adee0?hl=en&fwc=1">original one</a> of equal length: <CODE> s!.!y\$IVCXL91-80\$XLMCDXVIII\$dfor\$\$_.=4x\$&%1859^7 </CODE> used in the 2004 Polish golf tournament. </P> <P> <B>Update</B>: Here is a test program to verify that all four magic formulae are correct: <CODE> 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"; </CODE> </P> 594299 1009253