<?php
    $parent = get_cat_ID("photos");
    $cats = get_categories("child_of=".$parent);
    foreach ($cats as $cat) {
    query_posts("posts_per_page=1&orderby=rand&cat=".$cat->cat_ID);
?>
    <?php if ($parent == true && have_posts()) : while (have_posts()) : the_post(); ?>
        <ul>
            <?php if (has_post_thumbnail()) { ?>
                <?php
                    printf( '<li><a href="'.get_category_link($cat->cat_ID).'">'.get_the_post_thumbnail(get_the_ID(), "album-thumb").'</a><a href="'.get_category_link($cat->term_id).'">%s</a></li>',
                    apply_filters('get_term', $cat->name));
                ?>
            <?php } ?>
        </ul>
    <?php endwhile; endif; } ?>
    <?php if (! $parent == true || ! $cat == true) { ?>
        <p><?php _e("Sorry, no posts matched your criteria."); ?></p>
    <?php } ?>
<?php wp_reset_query(); ?>