Content

• To step
• Part 1 of 3: Playing Mastermind
• Part 2 of 3: Choosing a methodical approach
• Part 3 of 3: Example of a powerful methodical approach (2)
• Tips

Mastermind is a puzzle game in which a player tries to guess the code that the opponent comes up with. Mastermind was originally a board game, but was previously just a pen and paper game and is now available online and for mobile devices as well. You can also play Mastermind paper and pen if you don't have the standard game or the video game.

To step

Part 1 of 3: Playing Mastermind

1. Have one of the players come up with a code. Mastermind consists of a row of holes that are separate on one side of the board, hidden under a hinged lid. The person creating the code (from now on, the codemaker) takes a pair of colored pins and places them in that row of holes in random order. This is the code that the codebreaker will try to guess.
   • If you are playing a video game version, the computer will usually do this instead of a player.
   • The code maker must put a pin in each hole. He has the option to use more than one pin of the same color. He can, for example Green, Yellow and Blue put down.
2. Let the code breaker make a first guess. The other player, or the only player in video game versions, tries to guess what the hidden code is. Sitting on the other side of the board, the player takes the larger colored pins and places them in the nearest row of larger holes.
   • For example, the player would Blue, Orange, Green and Violet (your Mastermind game may have more holes or different colored pins).
3. Ask the code maker to provide feedback. Next to each "guess row" is a small square with enough holes for four small pins. These pins only come in two colors: white and red (or white and black in some versions). The code maker uses this to provide clues as to how good the guess was. The code maker must be honest, and always drop pegs using the following instructions:
   • Each white pin means that one of the guessed pins is correct, but is in the wrong hole.
   • Each red (or black) pin means that one of the guessed pins is correct, but in the wrong hole.
   • The order of the white and black pins does not matter.
4. Learn by examples. In our example above, the code maker secretly chose Yellow - Yellow - Green - Blue. The codebreaker guessed Blue - Orange - Green - Purple. The code maker looks at this guess to find out what hint he can give in pegs:
   • Pin # 1 is Blue. There is a blue pin in the code, but not at position # 1. This earns a white pin as a clue.
   • Pin # 2 is Orange. There is no orange in the code, so no pin is placed for it as a hint.
   • Pin # 3 is Green. There is a green pin in the code, in position # 3. This deserves a red (or black) pin as a hint.
   • Pin # 4 is Violet. There is no purple in the code, so no pin is placed for it as a hint.
5. Repeat this for the next row. The code breaker now has a bit of information. In our example, the player was given a white hint, a red hint and two empty holes. This means that of the four pins that the player has placed, one of them belongs in the row, but is not in the correct position, one is in the right place, and two of them are not in the code. The player can use this for his strategy and then make a second guess for the next highest row:
   • The code breaker guesses this time Blue - Yellow - Orange - Pink.
   • The code maker checks this guess: Blue right, but in the wrong place, Yellow is right and in the right place, Orange is not correct and Pink also not.
   • The code maker places one white hint pin and one red hint pin.
6. Continue until the code is guessed or the number of turns is up. The code breaker continues to guess, using information from all previous hints the player has been given. If the player manages to guess the entire code in exactly the right order, then the player wins the game. If the player fails to guess and has filled every row with pins, the code maker wins.
7. Switch places and play again. If you are playing a two-person game, turn the board over so that both players switch roles. This way, both players get the chance to play the most important part of the game: guessing the code.

Part 2 of 3: Choosing a methodical approach

1. Start with four of the same colors. A new Mastermind player quickly learns that even a gamble that yields multiple hints does not always lead to a quick win, as there are so many possible ways to interpret the hints. By starting with four pins of the same color (such as Blue - Blue - Blue - Blue) immediately gives you useful information to work with.
   • This isn't the only strategy in Mastermind, but it's an easy one to get started with. It won't work very well if your version has more than six colors to choose from.
2. Use 2x2 patterns to detect the colors. Your next steps are two color pairs, always starting with two color pairs you guessed earlier. For example: after Blue - Blue - Blue - Blue, you guess a sequence starting with Blue - Blue and end with a different color, until you know all the available colors. Here's an example:
   • Blue - Blue - Blue - Blue : No hint pins. That's fine, we'll continue to use Blue anyway.
   • ’Blue - Blue - Green - Green : A white pin. We keep in mind that the code has one green, and it must be in the left half.
   • Blue - Blue - Pink - Pink : One black pin. We now know that there is one pink in the code, in the right half.
   • Blue - Blue - Yellow - Yellow : a white pin and a black pin. There must be at least two yellow pins in the code, one on the left and one on the right.
3. Use the logic to rearrange the known pins. Once you've earned four hint pins in total, you'll know exactly which colors are involved, but not in what order. In our example, the code should contain green, pink, yellow, and yellow. The system of dividing the board into two pairs has also given us some information on what order to place the pins, so we should be able to figure this out in one to three turns:
   • We know that Green - Yellow - Pink - Yellow have a left half and a right half containing the correct pins, but it turns out that we get two white pins and two black pins in our results. This means that in either half, the pins must switch places (either # 1 and # 2, or # 3 and # 4).
   • We try Yellow - Green - Pink - Yellow and get four black pins - the code is fixed.

Part 3 of 3: Example of a powerful methodical approach (2)

1. Eliminate two colors at once (with four unknown pins). For example: red and blue:
   • Red - Red - Blue - Blue.
   • Result 1: No pins. Red and blue are not in the code
   • Result 2: A white or black pin (let's assume a white pin). Either there is red or blue in the code once. Blue - Blue - Blue -Blue gives you a pin if it's blue, or no pin if it's red (let's assume there are no pins). In the example we now know that there is a red pin, and that it is on the 3rd or 4th place (because we have a white pin at Red - Red - Blue - Blue). Finding it will be discussed in the following strategy (in one step: Red - Green - Green - Green ).
   • Result 3: more pins (let's assume two white pins). As with result 2, we can Blue - Blue - Blue - Blue try to figure out how many pins were blue (let's start from zero again). Now it's just a matter of finding the pins. In the example, we already know that the third and fourth are red pins, because there are two red pins, and the player is not in first or second place (because we got two white pins).
2. Determine the location of a red pin if you know that there is at least one red pin, but do not know which of the holes it should be in. You can find the correct pin by trying each of the locations. As an alternative color we use colors that we have not yet tested. In this way we not only find the red pin, but also additional information about other colors. The following is an example, if you know that there is a red pin, but you don't know which of the four holes it is in. It also gives you the number of green, yellow and pink pins.
   • Red - Green - Green - Green
   • Yellow - Red - Yellow - Yellow
   • Pink - Pink - Red - Pink
   • Note: If you know the exact amount of red pins, you don't have to try the last location: if there is one red pin, and it's not in the first, second or third location, it must be on the fourth.
   • Result 1: If there are no white pins, you have at least one black pin. That pin indicates that the red pin is in the right place.
   • Result 2: If there is one white pin, you know that the red pin is in the wrong place, and the alternate color is not in the code.
   • Result 3: If there is a second white pin, you know that the second color should be in place of the red pin.
   • Result 4: If there are one or more black pins, it indicates that the second color is present. It also gives you the number of pins of that color, and you know it's not where red is (because that would make a white pin), or, of course, where red would be.
3. Eliminate two colors at once (with three unknown pins). Put one color in the places you know, and the other color in the places you don't know. For example: green and yellow - we know the first pin is red:
   • Green - Yellow - Yellow - Yellow.
   • Result 1: no pins - green and yellow are not in the code
   • Result 2a: a white pin indicates that there is green in the code, but we don't know how many (it can be one, but also two or even three)
   • Result 2b: the number of black pins indicates the number of yellow pins in the code (as noted in Strategy 2: knowing the exact number of pins can save you one step in finding the right color)
4. Eliminate two colors at once (with only one or two unknown pins). This strategy is very similar to the previous strategy, but now the number of white pins also gives us the number of that color. For example: green and yellow - we know the first two pins are red:
   • Green - Green - Yellow - Yellow.
   • Result 1: no pins - green and yellow are not in the code
   • Result 2a: a white pin indicates that there is one green in the code, while two pins indicate that there is green in the code (since there are only two unknowns, it is impossible for there to be three greens)
   • Result 2b: As with the previous strategy, the number of black pins indicates the number of yellow pins in the code (as noted in Strategy 2: knowing the exact number can save you a step in finding the color)
5. Learn from an example. In this example, we start, as always, with strategy 1.
   • Strategy 1: Blue - Blue - Red - Red gives two white pins. So we know that red and / or blue are present. We want to know which one is blue and which one is red, so we check the following:
   • Strategy 1a: Blue - Blue - Blue - Blue gives a black pin. This means, as we know from the previous answer, that there is a blue (and in the wrong place - so the third or fourth), and therefore also a red (and also in the wrong place, so the first or second).
   • Strategy 2 (find blue): Green - Green - Blue - Green gives a white and a black pin. We tested one of the locations of blue, and since there is a white pin, we know it's not the third pin. Since we know it was either the third or fourth pin, we know that the fourth pin is blue. The black pin also indicates that there is a green pin, but it is not in third place (because it is a black pin and not a white one).
   • Strategy 2 (find red): Red' - Yellow - Yellow - Yellow indicates a single white pin, so while we know that red is in the first or second place, we now know that it is not the first place. So it is the second place. We also know that there is no yellow color.
   • The next color we had information on was green - but since we know that it is not the third place, and the second and fourth places are already filled with blue and red, we know it must be the first.
   • Strategy 4: Orange - Orange - Pink - Orange Indicates a white pin. So we know that the only unknown place - the third place - has an orange color.
   • Answer: Green - Red - Orange - Blue.

Tips

• If the code breaker guesses several of the same color, the code maker will still only give one hint for each pin. For example: as the code breaker Yellow - Yellow - Blue - Blue guess and the correct code is Yellow - Blue - Green - Green, then the code maker places a red pin (for the first yellow) and a white pin (for the first blue). The second yellow and second blue do not deserve hint pins, as the code only has one yellow and one blue in it.
• If you start guessing Blue - Blue - Green - Green (or any 2x2 pattern), and playing perfectly, you can always win in five moves or less. However, to play perfectly you have to consider all 1296 possible codes, so this strategy is only used by computers.
• To make the game more difficult, you can give the code breaker fewer turns.