1post per sub-cat

<?php //in a category archive, show one post per sub category, no duplicates, in three columns
//alchymyth 2011

$cat = get_query_var('cat');
$no_duplicates = array();

$sub_cats = get_categories('parent='.$cat); //get the direct sub categories
  if( $sub_cats ) :

    foreach( $sub_cats as $sub_cat ) :

    /*get the latest post of this subcat;
    for instance: output the category name, the post title, and the excerpt of one post*/
    $args = array(
    'posts_per_page' =>1,
    'category__in' => array($sub_cat->term_id),
    'post__not_in' => $no_duplicates
    );
    $cat_query = new WP_Query( $args );
        if( $cat_query->have_posts() ) : while( $cat_query->have_posts() ) :
        $cat_query->the_post();
        $no_duplicates[] = $post->ID; ?>

        <?php $column = ($column == '') ? 'columnleft' : (($column == 'columnleft') ? 'columnmiddle' : (($column == 'columnmiddle') ? 'columnright' : 'columnleft' )); // define the css class for the respective column ?>
        <div class="<?php echo $column; ?>">
            <h3>
        <a href="<?php echo get_category_link($sub_cat->term_id); ?>" title="View all posts filed under <?php echo $sub_cat->name; ?>"><?php echo $sub_cat->name; ?></a>
        </h3>

        <a href="<?php the_permalink(); ?>" rel="bookmark" title=" <?php the_title_attribute(); ?>" class="title"><?php the_title(); ?></a>

        <?php the_excerpt(); ?>

        </div>
        <!-- END <?php echo $column; ?> COLUMN -->

    <?php endwhile; endif; ?>

<?php endforeach; //ends: foreach( $sub_cats as $sub_cat )

  endif; //ends: if( $sub_cats ) ?>