Three men decided to split the cost of a hotel room. The hotel manager gave them a price of $30. The men split the bill evenly, each paying $10, and retired to their room.
However, the manager realized that it was a Wednesday night, which meant the hotel had a special: rooms were only $25. He had overcharged them $5!
He promptly called the bellboy, gave him five one-dollar bills and told him to return it to the men. When the bellboy explained the situation to the men, they were so pleased at the honesty of the establishment that they promptly tipped the bellboy $2 of the $5 he had returned and each kept $1 for himself.
The Problem: Each of the three men ended up paying $9 (their original $10, minus $1 back) totalling $27, plus $2 for the bellboy makes $29. Where did the extra dollar go?
The faulty reasoning lies in the addition at the end. 3 x $9 does equal $27, but the $2 tip is included in that $27, so it makes no sense to add the $2 to $27 to make $29. They paid $25 for the hotel room, $2 for the tip ($27), and then got $1 back each to make the original $30.