How to create a page with post from random category

If you already know how to create a page of posts, you can use this code to select a random category ID to use in the query:

// Select a random category ID
   $sql = "SELECT DISTINCT tr.term_taxonomy_id
      FROM $wpdb->term_relationships tr
      JOIN $wpdb->posts p ON (p.ID = tr.object_id)
      JOIN $wpdb->term_taxonomy tt ON (tt.term_taxonomy_id = tr.term_taxonomy_id)
      WHERE p.post_type = 'post'
      AND p.post_status = 'publish'
      AND tt.taxonomy = 'category'
      AND tt.term_taxonomy_id <> 1
      ORDER BY RAND()";
   $cat = $wpdb->get_var($sql);
   echo "CAT = $cat<br />";  // Use this for testing