Medium
logic-puzzlesmathematical-reasoningmisleading-problems

The Missing Dollar Logic Puzzle Explained

Problem Statement

Three people check into a hotel room that costs $30. They each pay $10. Later, the manager realizes the room only costs $25 and gives $5 to the bellhop to return. The bellhop keeps $2 and gives each person $1 back. Now each person paid $9 (total $27) and the bellhop has $2 (total $29). Where is the missing dollar?

Answer

There is no missing dollar — the math is misleading

Step-by-Step Explanation

  1. 1

    This puzzle uses misleading arithmetic to create a false problem.

  2. 2

    Let's track the money correctly:

  3. 3

    Initial payment: 3 × $10 = $30

  4. 4

    Actual room cost: $25

  5. 5

    Manager gives bellhop: $5

  6. 6

    Bellhop keeps: $2

  7. 7

    Bellhop returns: $3 (3 × $1)

  8. 8

    Correct accounting:

  9. 9

    - Guests paid: $27 total ($9 each)

  10. 10

    - Hotel has: $25

  11. 11

    - Bellhop has: $2

  12. 12

    - Total: $25 + $2 = $27 ✓

  13. 13

    The error: The puzzle adds the bellhop's $2 to the $27, but the $2 is already included in the $27.

  14. 14

    The $27 the guests paid = $25 (hotel) + $2 (bellhop).

  15. 15

    There is no missing dollar — it's a trick of misleading addition.