Once, a group of Russian professors gathered at a restaurant to celebrate the end of the term. The restaurant was very fancy and expensive. They were all very excited to dine there. They were shown their table. Just then unexpectedly, the group started arguing as to who would sit at the head of the table. Each professor wanted that particular seat. I think I have an idea said the geography professor. We can sit based on geographical location, “Since I am from a village in the northernmost part of Russia, I should sit at the head.” Another professor proposed sitting alphabetically, saying, “My name starts with A, so I will sit at the head.” As they debated, their voices grew louder, disturbing other guests. Concerned about the commotion, the manager grew anxious. Sensing the tension, a waiter intervened, proposing a solution.
“I’ll assign each of you a seat today,” the waiter suggested. “You sit where I ask you to sit. Next time you visit, sit in a new arrangement, making sure you don’t sit in the same seat as today. Keep doing this until the day you repeat today’s setup. When that happens, your meal will be on the house!”
Thrilled at the prospect of a free meal, the professors eagerly agreed. The waiter showed each of them their seat around the table, and they happily agreed and had a good time.
Later, the manager confronted the waiter, puzzled by the promise. “Why did you offer them a free meal?” the manager asked.
“Simple,” the waiter replied with a grin. “With ten professors, it would take ages for them to repeat today’s seating arrangement. How? We have 10 professors who need to sit at a table without repeating their arrangement. Each arrangement can be seen as a permutation of the 10 professors. The number of possible arrangements can be calculated using factorial notation. For 10 professors, the number of arrangements is 10! (10 factorial). 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800. So, there are 3,628,800 possible seating arrangements for the 10 professors.
If they come every day, how many days will it take for them to repeat a seating arrangement? Since there are 3,628,800 possible arrangements and they visit once a day, it will take 3,628,800 days for them to repeat today’s seating arrangement. Converting days to years: 3,628,800 days ÷ 365 days/year ≈ approximately 9,946 years. So u see 9946 years would go by before the ten professors repeat a seating arrangement and get a free meal every day. And that will surely not be possible. You are smart. What do you do? When I’m not waiting tables, I study math at the university:)
