Three engineers and three mathematicians are traveling by train to a
conference. At the station, the three mathematicians each buy
tickets and watch as the three engineers buy only a single ticket.
"How are three people going to travel on only one ticket?" asks a
mathematician.
"Watch and you'll see," answers an engineer.
They all board the train. The mathematicians take their respective
seats, but all three engineers cram into a restroom and close 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, the mathematicians 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. To their astonishment, the
engineers don't buy a ticket at all.
"How are you going to travel without a ticket?" asks one perplexed
mathematician.
"Watch and you'll see," answers a 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 afterward, 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."
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