display unique post per category

by

Track your post IDs.

$cat_args = array(
  'orderby' => 'name',
  'order' => 'ASC',
  'exclude' => '17,1',
  'number' => '6'
);

$fcategories = get_categories($cat_args);
$used_ids = array();
foreach($fcategories as $fcategory) {
  $post_args = array(
    'posts_per_page' => 1,
    'cat' => $fcategory->cat_ID
  );
  if (!empty($used_ids)) {
    $post_args['post__not_in'] = $used_ids;
  }

  $fposts = new WP_Query($post_args);
  if ($fposts->have_posts()) {
    while($fposts->have_posts()) {
      $fposts->the_post();
      $used_ids[] = $post->ID;
      get_template_part('post', 'homepage');
    }
  }
}

A couple of notes:

  1. There are a couple of syntax errors in your code

  2. Don’t use query_posts.

    It should be noted that using this to replace the main query on a page
    can increase page loading times, in worst case scenarios more than
    doubling the amount of work needed or more    . While easy to use, the
    function is also prone to confusion and problems later on. See the
    note further below on caveats for details.

    http://codex.wordpress.org/Function_Reference/query_posts (emphasis mine)