# The Disappearing Dollar

Three co-workers are on a business trip. They arrive at their hotel only to learn their reservations have been lost. The desk clerk tells them there is only one room still available but it can be shared by the three companions. The cost of the shared room is $30 (this is an old puzzle :). Reluctantly, they each chip in $10 and take the room. After settling in, the manager finds out about the situation and instructs the desk clerk to provide a reduced rate of $25, as compensation for the guests’ trouble. The clerk sends a clever bellhop to refund the $5 overpayment. Realizing $5 can’t be evenly divided by the three room occupants, the bellhop pockets two dollars and returns $3 to the roommates, each of whom happily accepts his $1 discount.

To summarize, each traveler paid (10 – 1) = $9 so the three roommates together paid $27 and the bellhop kept $2 for a grand total of $29. But the initial outlay was $30. What happened to the missing dollar???

[Post your answer in a comment below. Comments will be hidden for now to avoid spoiling the answer but on Sunday night I’ll post the correct solution and make all comments visible.]

Solution: This is a bit of arithmetic sleight of hand – there is no missing dollar. To see why, let’s examine the two transactions:

EVENT GUESTS HOTEL BELLHOP TOTAL After Check-In -$30 $30 0 0 After Rebate -$27 $25 2 0 After the rebate, the initial payment of $30 is irrelevant. The final payment of $27 is the amount that needs to be reconciled, which it is by adding the hotel’s $25 take and the $2 pocketed by the bellhop. Hat’s off to Sudhakar, Simon and Morag for solving the puzzle correctly. Dan gets the prize for most creative guess. :)