The Missing Dollar Riddle: A Classic Trick Question Explained

The "missing dollar" riddle is a classic brain teaser that often leaves people scratching their heads. It's a deceptively simple problem that plays on our intuitive way of thinking about money. Let's break it down and see why the answer isn't as mysterious as it seems.

The Riddle

Three friends check into a hotel room. The clerk tells them the room is $30, so each friend pays $10. Later, the clerk realizes the room should only have cost $25. He gives the bellhop $5 to return to the friends.

On the way to the room, the bellhop realizes he can't divide the money evenly. He pockets $2 and gives each friend $1 back.

Here's the tricky part: Each friend effectively paid $9 for the room ($10 initial payment - $1 back). That's a total of $27. The bellhop kept $2. If you add those together, you get $29. Where did the missing dollar go?

The Solution

The riddle tricks us by making us focus on the wrong calculations. The problem is in how we're adding the money. Here's the correct way to think about it:

• **Hotel's Earnings:** The hotel actually received $25 for the room.
• **Bellhop's Take:** The bellhop kept $2.
• **Friends' Cost:** Each friend effectively paid $9, totaling $27.

The $27 the friends paid covers the $25 room cost and the $2 the bellhop kept. There is no missing dollar. The error comes from adding the bellhop's earnings to the friends' total cost, which is a double-counting of the money.

Why It's So Tricky

The riddle plays on our tendency to focus on the immediate numbers and make quick calculations. We get caught up in the idea that the friends paid $27 and the bellhop kept $2, making it seem like a dollar is missing. However, the problem lies in our framing of the situation. The $27 the friends paid is not separate from the $2 the bellhop kept – it's all part of the same transaction.

Key Takeaways

• Careful with Calculations: This riddle highlights the importance of being careful with how we add and subtract numbers, especially when dealing with money.
• Think Clearly: It's essential to break down problems into their component parts and avoid making assumptions.
• Beware of Misdirection: Trick questions often rely on misdirection to lead us to incorrect conclusions. Stay focused on the core information and avoid getting sidetracked by irrelevant details.

The missing dollar riddle is a fun and engaging way to learn about the importance of clear thinking and logical reasoning. It's a reminder that even simple problems can be deceptive, and it's always a good idea to double-check our calculations and assumptions before coming to a conclusion.