I love a good logic trap. If you’re looking for a classic “deceptive” brain teaser that forces people to question their basic arithmetic, the Missing Dollar Riddle is the gold standard.
It’s the perfect blend of simple math and linguistic sleight-of-hand.
The Setup
Three guests check into a hotel room that costs $30. They each contribute $10 and head up to their room.
A few minutes later, the clerk realizes the room is actually on sale for $25. He hands the bellboy five $1 bills to return to the guests.
On the way to the room, the bellboy realizes he can’t divide $5 equally among three people. He decides to keep $2 as a tip and gives $1 back to each of the three guests.
The Logic Trap
Now, let’s look at the math from the guests’ perspective:
- Each guest originally paid $10 but got $1 back, so they each spent $9.
- Total spent by the three guests: $3 \times 9 = \mathbf{\$27}$.
- The bellboy kept $2.
- $27 + 2 = \mathbf{\$29}$.
Where is the missing dollar?
The Solution (The “Aha!” Moment)
The deception lies in how the numbers are added, not in the math itself.
In accounting, you don’t add “expenses” to “theft” to get a total; you subtract them from the original amount. The $27 the guests paid already includes the $2 the bellboy kept.
- The Room: $25
- The Tip: $2
- Total Spent: $27
The other $3 is in the guests’ pockets. Adding the $2 tip to the $27 total is a logical fallacy—it’s like saying, “I spent $27, and I have $2 in my pocket, so where is the other dollar?” No, you spent $27, and $25 went to the hotel while $2 went to the bellboy.
Do you want to try to solve another one, or should I throw a different kind of logic puzzle your way?