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

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


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$$_.=5x$&*8%29628
don't forget about Ton's original one of equal length:
s!.!y$IVCXL91-80$XLMCDXVIII$dfor$$_.=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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