Minute Mystery: The Code Puzzle

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

 

 

The Code Puzzle

Category: Logic, Number Puzzle

A 3‑digit vault code uses three distinct nonzero digits.

  • The sum of the digits is 15.

  • The first digit is twice the third digit.

  • The middle digit is prime.

What is the code?

 

 

Solution

Let the code be “ABC”:
  • A + B + C = 15
  • A = 2 × C
  • B = 2 / 3 / 5 / 7

Substitute A with 2C

  • 2C + B + C = 15
  • 3C + B = 15
  • B = 15 – 3C

Test C, based on B = 15 - 3C

  • C = 1 / 2 / 3 / 4 (since 2C ≤ 9)
  • C = 1 → B = 12 (no)
  • C = 2 → B = 9 (no)
  • C = 3 → B = 6 (no)

  • C = 4 → B = 3 (yes, prime)

If C = 4 and B = 3, then

  • A + 3 + 4 = 15
  • A = 15 - 7
  • A = 8

Answer: The code is 834

 

 

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