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choroba's Explore-all-possible-combinations mechanism works okay for smallish sets (max:32 or 64 depending upon your Perl), but will get very slow for anything much larger than 20 or so.

This will very quickly (less than 0.001 of a second) find a solution, if one exists, for sets of 100s or 1000s of elements. :

```#! perl -slw
use strict;
use Time::HiRes qw[ time ];
use List::Util qw[ sum ];

sub partition {
my \$sum = sum @_;
return if \$sum & 1;
\$sum /= 2;
my @s = sort{ \$b <=> \$a } @_;
my @a;
my( \$t, \$n ) = ( 0, -1 );
\$t + \$s[\$n] <= \$sum and \$t+= \$s[\$n] and push @a, \$n while ++\$n < @
+s and \$t <= \$sum;
@a = delete @s[ @a ];
@s = grep defined, @s;
return unless sum( @a ) == sum( @s );
return \@a, \@s;
}

our \$N //= 64;

my( \$a, \$b ) = partition 1,3,5,7;
print "sum( @{ \$a } ) == sum( @{ \$b } )" if \$a;

my @set = map int( rand 100 ), 1 .. \$N;

my \$start = time;
( \$a, \$b ) = partition @set;
printf "Took %f seconds\n", time() - \$start;

if( \$a ) {
printf "(%u) == sum( @{ \$a } ) == sum( @{ \$b } )\n", sum @\$a;
}
else {
print "No solution existed for the \$N element set @set";
}

A few runs:

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