Add hint cooldown and raise player limit to 15

- Lock hint button for 10s per riddle with live countdown display
- Clear hint timer when player finishes their race
- Raise max players from 8 to 15 with 15 distinct player colors

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

public/index.html

@@ -43,7 +43,7 @@
         <div id="error-msg" class="error-msg"></div>
       </div>
 
-      <p class="home-footer">Up to 8 players &bull; Answer 10 riddles to cross the finish line</p>
+      <p class="home-footer">Up to 15 players &bull; Answer 10 riddles to cross the finish line</p>
     </div>
   </div>