In the game of $Mindmaster$, secret codes are created by placing pegs of any of seven different colors into four slots. Colors may be repeated, and no slot may remain empty. How many secret codes are possible?

Question

Computers and Technology

Riley Banks

7 August, 22:42

In the game of $Mindmaster$, secret codes are created by placing pegs of any of seven different colors into four slots. Colors may be repeated, and no slot may remain empty. How many secret codes are possible?

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Addisyn Morales · Answer 1

In the game of $Mindmaster$, secret codes are created by placing pegs of any of seven different colors into four slots. Colors may be repeated, and no slot may remain empty. 2401 secret codes are possible.

Explanation:

Mastermind is a board game that was developed by Mordecai Meirowitz, in 1971. The Code maker sets a secret code, then the Codebreaker attempts to meet the code using logic, deduction. Behind each move, the Code maker provides hints to the Codebreaker. Make the code even more indirect by using multiple pegs of the same color or by leaving one or more peg holes empty. With so many feasible code sequences, every game is confirmed to be a brain teaser.

7 colors with 4 slots and repetition of color are accepted so 7^4 is 2401.