The Cinema Queue
One rainy Saturday evening some years ago in lower Manhattan, Jane, a ticket girl, rushed into the booth of the Roxy movie theatre to prepare things for the night shift.
As usual, Eusebio, the evening shift ticket seller, had left the booth in a mess, with an ashtray full of thin butts, and Jane was shocked to see the cash register empty – no bills to give change with.
Jane looked up to see some Japanese tourists lining up to buy tickets for the five-dollar late movie of the evening “The Seven Samurai”, when a toothy, smiling and bowing Japanese who seemed to be the tour guide stuck his face in into the ticket window.
“Kon’nichiwa, me Mr. Fujimori. We ten tourist from Osaka, see samurai movie. Half have 10 dollar bill, other half have five dollar bill. You give change, buy ticket, no problem, ok?”
“Sure, Mr. Fujimori, I’ll do what I can to give you all correct change,” said Jane politely, feeling a mounting panic, knowing that the cashbox was empty.
“What shall I do, what shall I do…” spun around in her head, “What if the first person to buy a ticket gives me a ten dollar bill? I won’t have any change to give back.”
Then Jane got a bright idea, which she implemented with the aid of Mr. Fujimori, and all tickets were sold with correct change given so that Jane ended up with fifty dollars in the till.
What would you say was the bright idea Jane got to solve this problem?
What would be the probability of successfully terminating each ticket transaction without any problems giving change if the Japanese in the queue had been lined up at random?
Tags: queue combinations, queues