Minute Mystery: The Locked Box

Bite-sized brain teaser to solve in a minute or less.

 

 

The Locked Box

Category: Logic, Number Puzzle

A mysterious locked box requires a 3-digit code to open. You know the following:

  1. The code uses the digits 1, 2, and 3, each exactly once.
  2. The code is odd.
  3. The number is greater than 200.
  4. The tens digit is less than the units digit.

What is the code?

 

 

Solution

  • List all permutations of 1, 2, and 3 that form a 3-digit number:
    • 123, 132, 213, 231, 312, 321.
  • From Clue 2: For the number to be odd, the units digit must be 1 or 3, eliminating 132 and 312.
  • From Clue 3: The number must be greater than 200, so exclude 123.
    This leaves 213, 231, and 321.
  • From Clue 4: The tens digit must be less than the units digit. In 213, tens digit 1 is less than units digit 3; in 231, tens digit 3 is not less than 1; in 321, tens digit 2 is not less than 1.

The code is 213.

 

 

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