It is a dark and stormy night when three travelers must stop in hotel. They approach the front desk, where the front desk clerk informs them of the rate of $30 for three men in one room. The men each hand over a $10 bill for a total of $30. They are given a key and go to their room. Moments later, the manager is informed of the transaction and reprimands the clerk, reminding him of the 3 men/1 room special of $25 a night.

The manager asks the clerk to refund the $5 to the men. Taking five $1 bills from the register, he goes to the men's room and knocks on the door. While he waits for the men to come to the door, he realizes a problem. How can he divide the 5 $1 bills evenly among the men? When they answer the door, he tells them that there was a special that night and that the total bill only came to $27. He gave them each $1 as a refund, and the sneaky clerk made off with $2 for himself.

Though it seems everyone came out a winner, a problem occurs. In the beginning, $30 was paid. In the end, however, the man had paid a collective $27, and the clerk had $2. $27 + $2 =$29, not $30. The question is: where is the extra dollar?

This is a cleverly-disguised case of subtracting apples from oranges.

It's obvious that no dollar disappeared, and misleading to demonstrate that $27 + 2 = $29.

Here's a couple of ways to make this more clear:

  • There was originally $30 in the world. Now the men each have $1, the manager has $25, and the clerk has $2. 3 + 25 + 2 = 30.
  • Consider that the men each paid $9 (net). Then there's $27 dollars in the hotel: $25 in the manager's cash register and $2 in the sneaky clerk's pocket.
It all adds up.

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