This isn’t a joke; rather it’s an interesting problem.

Three mathematicians went to a convention. They needed a room, but all the hotels were full. They finally found a motel that had a vacancy. They told the Innkeeper they needed rooms. The Innkeeper said “I’ve only got one room left.”

The three mathematicians said “We’ll take it.”

“That’ll be $30.00.”

The mathematicians each pulled out 10 $1 bills; they handed to collected $30 to the Innkeeper and went to their room.

After a while, the Innkeeper thought to himself “I’ve overcharged those three men. I should give them a discount for having to share one room.” He called the bellboy over and told him: “Take this money to room 303 and tell the three men there I’m giving them a discount for having to share a room.” He handed the bellboy five one dollar bills.

The bellboy took off to the three men’s room. On the way, he thought,* How are three men going to split $5? I can help them out by giving them just three dollars*. So, in the spirit of altruism (obviously) the bellboy quietly pocketed two of the dollar bills. When he got to the room, he rang the bell and when one of the mathematicians answered, he said “The Innkeeper said to tell you he is sorry for the inconvenience, and offers this refund for your hardship.”

He then handed the man three one dollar bills and left. The mathematician gave a dollar to each of his companions, and the three went to sleep.

So what’s the problem?

Since each of the mathematicians received $1 back from the bellboy, each man paid only $9 apiece for the room. That is, they paid only $27 for the room. The bellboy has $2 in his pocket. This accounts for $29 of the original $30 paid.

What happened to the missing dollar?