Three friends check into a hotel room that costs $30. They each contribute $10, totaling $30, and pay the hotel manager. Later, the hotel manager realizes that there was a promotion, and the room should only have cost $25. The manager gives $5 to the bellboy and asks him to return it to the friends.

The bellboy, however, decides to keep $2 for himself and gives $1 back to each of the three friends. Now, each friend has paid $9 ($10 originally paid minus the $1 returned), and the bellboy has $2.

If you add up the $9 each friend paid, you get $27. Adding the $2 the bellboy kept brings the total to $29. But they originally paid $30. So, where is the missing dollar?

Objective:
Solve the riddle and explain where the "missing" dollar went.

Solution

The riddle presents a classic scenario of misdirection, where the logic appears sound, but the way the numbers are combined is flawed. To solve this, let’s break down the scenario and follow the money logically.

Step-by-Step Solution for Missing Dollar Puzzle:

Step 1: Understand the Total Money Paid

• The three friends initially paid $30 to the hotel manager.

Step 2: Apply the Promotion Adjustment

• The room should have only cost $25, so the hotel manager gives $5 to the bellboy to return to the friends.

Step 3: Consider the Bellboy’s Actions

• The bellboy decides to keep $2 and gives $3 back to the friends ($1 to each).

Now, let’s break down the amounts logically:

• Friends' Net Payment:
  Each friend originally paid $10, and each received $1 back, so their net payment is $9.
  • Total paid by the friends: 3 friends × $9 = $27.
• Money Distribution:
  • Out of the $27, $25 goes to the hotel for the room.
  • The remaining $2 goes to the bellboy.

This breakdown accounts for the full $27: $25 for the room + $2 kept by the bellboy.

Step 4: Address the Misleading Addition

The riddle misleads by suggesting that you should add the $2 kept by the bellboy to the $27 total, which incorrectly suggests there’s a missing dollar. However, this addition is logically incorrect because the $27 already includes the $2 that the bellboy kept.

The correct way to look at it is:

• Total amount originally paid by the friends: $30.
• Amount kept by the hotel for the room: $25.
• Amount kept by the bellboy: $2.
• Amount returned to the friends: $3 ($1 each).

No money is missing; the riddle is just a clever play on how the numbers are presented.

Final Answer

There is no missing dollar. The friends paid a total of $27, which includes the $25 for the room and $2 kept by the bellboy. The confusion arises from the incorrect addition of the $2 kept by the bellboy to the $27.