Looks like we may need benchmark for this game. Here is the answer, I'll post the complete code in 24 hours so as not to spoil all the fun. It's ~ 30 average lines long and runs under strict. I have included the begining and end. My woodwork teacher used to say look after the edges and the middle will look after itself..... BTW Please enter perlmonks for the prize and donate it to the offering plate when we win!

Hint:

There is only one solution,

brute force is not the key

With code in evolution,

consider the holy three

tachyon

one 435 three 17955 six 820 ten 153
Elapsed 0 seconds

#!/usr/bin/perl -w
use strict;
my $time = time();
my %tri;

# make hash of tiangular numbers 5 digits or less
map{$tri{.5*$_*($_+1)}=1}1..446;
...
...
# prove we are right!
print "one $o$n$e " if defined $tri{"$o$n$e"};
print "three $t$h$r$e$e " if defined $tri{"$t$h$r$e$e"};
print "six $s$i$x " if defined $tri{"$s$i$x"};
print "ten $t$e$n\n" if defined $tri{"$t$e$n"};
 
$time = time()-$time;
print "Elapsed $time seconds\n";
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