Code Breaker

Goal

Find the secret combination of coloured pegs in as few guesses as possible. After each guess, the code-keeper answers with small pegs:

• Black: a peg of the right colour in the right place.
• White: a peg of the right colour, but in the wrong place.
• The order of the small pegs does not tell you which pegs they refer to.

How to play

• Tap a colour in the palette (or drag it onto a hole) to fill the current row; tap a peg to remove it.
• On the keyboard: digits 1 to 8 for the colours, Backspace to erase, Enter to confirm.
• Format: 4 pegs and 6 colours, or 5 pegs and 8 colours. “By level” picks the first up to the Intermediate level, the second after that.
• A colour may appear several times in a code (except in the AI’s code at the Beginner level).

Who guesses?

• You: the AI hides a code; find it before you run out of guesses.
• The AI: make up your code, then score each of the AI’s guesses with the “right place” and “wrong place” buttons (the game checks your scoring). The AI has 6 guesses in 4 × 6 and 8 guesses in 5 × 8: if your code holds out, you win.
• Duel: each player hides a code and guesses the other’s, taking turns. The first to find it wins; if you both need the same number of guesses, it is a draw.

About the AI

The solver applies Knuth’s algorithm: for each possible guess, it groups the codes that are still consistent by the answer they would produce, then picks the guess whose worst group is smallest (minimax), preferring a code that is itself consistent. In 4 × 6, a precomputed table of the 1,679,616 answers makes the calculation instant and guarantees a solution in five guesses at most. In 5 × 8 (32,768 codes), it samples guesses within a time limit. At the Beginner to Intermediate levels, the AI reasons like a human player: it remembers most of its clues at the Intermediate level, a little under half at the Amateur level and a quarter at the Beginner level, and sometimes tries a code without checking them. The hint uses the full solver.