Here's an implementation with simpler calculations, with fewer special cases and which can easily be extended to four columns.

It also fixes some bug in yours. Yours skips the 17th element ($dupes[16]) when you have 23 elements (@dupes == 23). I didn't track down the cause of the error.

The idea is simple: Pretend the array is a 2d array, then combine the row and col indexes into one.

my @dupes = qw( a b c d e f g h i j k l m n o p q r s t u v w );

my $num_cols = int( @dupes / 10 ) + 1;
if ($num_cols > 3) {
   $num_cols = 3;
}

my $num_rows = int( $#dupes / $num_cols ) + 1;

for my $r ( 0 .. $num_rows-1 ) {
   for my $c ( 0 .. $num_cols-1 ) {
      my $i = $r + $c * $num_rows;
      last if $i > $#dupes;
      print("\t$dupes[$i]");
   }
   print("\n");
}
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Update: Added "The idea ..." paragraph.