At the train station, the three mathematicians each buy a ticket, and then they watch as the three engineers buy only a single ticket between them.
Looking very puzzled, one of the mathematicians asks the engineers: “How are three people going to travel on only one ticket?”
“Watch and you will see,” answers one of the engineers.
A few minutes later, their train arrives at the platform, and they all get on board.
The mathematicians find seats in one of the carriages, but are curious to see all three engineers cramming themselves into one of the restrooms and closing the door behind them.
Shortly after the train has departed, the conductor comes around collecting tickets. He knocks on the restroom door and says, “Ticket, please.” The door opens just a crack and a single arm emerges with a ticket in hand. The conductor takes it and moves on.
The mathematicians see this and agree it is quite a clever idea, so after the conference, they decide to copy the engineers on the return trip and save some money (being clever with money, and all that).
When they get to the station, they buy a single ticket for the return trip, but to their astonishment, the engineers don’t buy a ticket at all.
“How on earth are you going to travel without a ticket?” asks one perplexed mathematician.
“Watch and you will see,” answers an engineer.
When they board the train, the three mathematicians cram into one restroom and the three engineers cram into another one nearby.
The train departs.
Shortly afterwards, one of the engineers leaves his restroom and walks over to the restroom where the mathematicians are hiding.
He knocks on the door and says, “Ticket, please.”
Image used under a Collective Commons License from: https://commons.wikimedia.org/wiki/File:Metropolitan_Railway_carriage_(first_class_interior)_(9129237231).jpg