1 post per cat with excludes

<?php // cycle through categories, print 1 post for each category

$exclude = '1'; //exclude 'uncategorized'//
$lastpost = get_posts('numberposts=1'); //get the last post
$last_cats = get_the_category($lastpost[0]->ID); //get the categor(y/ies) from the last post and add to the exclude list//
foreach($last_cats as $last_cat) {
$exclude .= ','.$last_cat->term_id;
}
$categories=get_categories('orderby=name&order=ASC&exclude='.$exclude);

  foreach($categories as $category) {
      $posts=get_posts('showposts=1&cat='. $category->term_id);
      if ($posts) {
        echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
        foreach($posts as $post) {
          setup_postdata($post); ?>
          <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
          <?php
        } // foreach($posts
      } // if ($posts
    } // foreach($categories
?>