How to Display a Single Post Excerpt

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the_excerpt() is one of a few template tags that do not accept a post ID as a parameter. Instead, you need to set up the global $post, run your tags, then restore it:

if ( $_post = get_post( 10 ) ) {
    setup_postdata( $post = $_post );
    the_excerpt();
    // Any other template tags for this post
    wp_reset_postdata();
}