My solution was correct. But the printing of my solution was incorrect. Here is the corrected solution. 
#! /usr/bin/perl -w
use strict;

my @numbers = @ARGV ? @ARGV : qw(2 8 4 5);

# Scores is a 2-dim array, $scores[$i][$j] is the best score
# that you can get given a string of $j numbers starting at
# $numbers[$i].
my @scores;
for (0..$#numbers) {
  $scores[$_][1] = $numbers[$_];
}

for my $j (2..@numbers) {
  for my $i (0..(@numbers - $j)) {
    my $a = $numbers[$i] - $scores[$i+1][$j-1];
    my $b = $numbers[$i+$j-1] - $scores[$i][$j-1];
    $scores[$i][$j] = ($a > $b) ? $a : $b;
  }
}

my $i = 0;
my $score = 0;
for my $j (reverse 1..$#numbers) {
#  print "@numbers[$i..($i+$j)]\n";
  if ($numbers[$i] - $scores[$i+1][$j] > $numbers[$i+$j] - $scores[$i]
+[$j]) {
    print "shift $numbers[$i]\n";
    $score = $numbers[$i] - $score;
    $i++;
  }
  else {
    print "pop $numbers[$i+$j]\n";
    $score = $numbers[$i+$j] - $score;
  }
}

print "shift $numbers[$i]\n\n";
$score = $numbers[$i] - $score;
$score *= -1;
print "Score: $score\n";
print "Best score: $scores[0][scalar @numbers]\n";

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In reply to Re^2: Puzzle: Given an array of integers, find the best sequence of pop / shift... by tilly
in thread Puzzle: Given an array of integers, find the best sequence of pop / shift... by TedPride

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