The Wednesday Luncheon Club, consisting of ten members, decided to celebrate its first anniversary by having lunch at a fancy restaurant. When the members arrived and were ready to take their seats, they could not decide where to sit.

Just when they were ready to leave because of their embarrassment at being unable to decide how to sit around the rectangular table, the manager came to the rescue and told them to sit down just where they were standing. Then the secretary of the club was to write down where they were sitting, and they were to return the following day and sit in a different order. If they continued this until they had tried all arrangements, the manager would give them anything on the menu, free of charge.

It sounded like a very good deal, so they agreed. However, the day of the free lunch never came. Can you explain why?