Change the first while to a foreach and remove the angle brackets from around @source and it'll work.

#!/usr/bin/perl -w
use strict;
open (SOURCE, '<', 'test.txt') || die "Can't open test.txt: $!";
my @source = <SOURCE>;
close (SOURCE);

my $size=0;
foreach(@source){
  $size++ while m{\b\w+\b}g;
}

print "wordcount: $size words\n";
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