How Many Codes in Mastermind? | 4 Pegs, 6 Colors

The classic Mastermind board game asks you to crack a hidden code. Before you can develop a strategy, it helps to understand exactly how many possible codes you are up against.

How Many Possible Codes in Mastermind?

The standard version of Mastermind uses 4 pegs and 6 colors, and duplicate colors are allowed (the same color can appear more than once in the code).

The answer: 6 × 6 × 6 × 6 = 6⁴ = 1,296 possible codes.

Each peg can independently be any of the 6 colors. With 4 pegs and no restrictions, that gives you 1,296 distinct combinations.

If Duplicates Were Not Allowed

If each color could only appear once (no repeats), the math changes:

6 × 5 × 4 × 3 = 360 possible codes.

You would choose any color for the first peg (6 options), then any remaining color for the second (5 options), and so on. In the standard game, however, duplicates are allowed, so the answer is 1,296.

A Quick Reference Table

The "Master" difficulty version (5 pegs, 8 colors, duplicates) has 32,768 possible codes — dramatically harder.

Why This Number Matters for Strategy

Knowing there are 1,296 codes is not just trivia. It is the foundation of optimal Mastermind strategy. The goal of each guess is to eliminate as many possible codes as possible, using the feedback (black pegs = right color, right position; white pegs = right color, wrong position).

Knuth's Algorithm

In 1977, mathematician Donald Knuth proved that any Mastermind code can be cracked in five guesses or fewer using an optimal strategy. Here is how it works:

1. First guess: Always start with 1122. This guess (two of one color, two of another) eliminates the most possibilities on average.
2. Use the feedback to eliminate codes. After each guess, remove all codes from your mental list that would not have produced the same feedback pattern.
3. Pick the guess that minimizes the worst case. Choose your next guess to maximize the number of codes eliminated, regardless of what feedback you receive.

Knuth's algorithm guarantees a solution within 5 guesses. In practice, most codes are cracked in 4.

A Simpler Rule of Thumb

If you do not want to run the full algorithm in your head, follow these guidelines:

• Spread colors. Your first guess should use 4 different colors to get the most information.
• Eliminate, do not confirm. A guess that could be right but tells you nothing new is wasted. Prefer guesses that split the remaining possibilities roughly in half.
• Use all feedback. Black pegs and white pegs are both crucial. A response of "0 black, 0 white" tells you that none of the colors in your guess appear in the code at all — a huge elimination.

The Probability Angle

With 1,296 possible codes and an optimal first guess, the feedback you receive narrows the field:

• Best case: You get "4 black, 0 white" on your first guess (you solved it in one!). Probability: 1/1296 ≈ 0.077%.
• Worst case with optimal play: You need 5 guesses (guaranteed maximum with Knuth's algorithm).
• Average case with optimal play: About 4.34 guesses.

Play Mastermind Free Online

Ready to put this knowledge to work? Play Mastermind free on PlayBrain — no download, no sign-up. Our version uses the classic 4-peg, 6-color format with full feedback (black and white pegs). You have 10 guesses to crack the code.

If you enjoy logical deduction games, also try Binary Puzzle, Logic Gates, KenKen, or Sudoku for similar brain challenges.