How many codes in mastermind

Some solutions might not be possible, or there might be a faster alternative. You evaluated the different possibilities and chosen the best solution to solve the problem with. Now it is time to execute the solution. You place the diamonds in the order that matches your solution to find out if you are right. The execution of your solution will lead to the desired results, or you have to think of a new solution to solve the problem.

Did you receive all green dots as feedback during Mastermind? You solved the code. Then it is time for a new solution. You know the code exists out of four diamonds, and there are five colours to choose from.

By placing three of the diamond in the same position as your first attempt and switching one colour, you can evaluate the fourth diamond. If you switch just one colour and you will receive three yellow dots, you know that the colour you switched was correct in the first attempt. If there are two yellow dots and two green ones, it means that the last diamond is in the correct place.

This means in our case, that the yellow diamond is on the correct place. In our example, the first situation happened. This means that our red diamond was part of the code and in the correct place. Next, you will have to figure out which of the other three diamonds of your first attempt does not belong to the code. The easiest way to do this is by using the same tactic in the second attempt.

You now know the red diamond is placed correctly, on the right. After repeating two diamonds like the first try, we put the yellow diamond on the remaining sport. In the example, you can see how this tactic is done during the third and fourth attempt. At attempt four, you know blue, yellow, green and red are part of the code. The encoder must respond by indicating whether one or more colors are correctly or incorrectly placed.

If the decoder finds the combination of the encoder, the game ends. The dCode solver uses an easy syntax to describe the combinations proposals and to deduce the possible solutions. Separate each proposition with a line break. Each letter represents a color of your choice, it is advisable to use the initial letter of the color but beware of duplicates : do not put B for both Black and Blue!

Prefer to replace Blue with C for Cyan. Example: Combination RGBY 2 0 correspond to a proposal with in position 1: R for Red, in position 2: G for Green, in position 3: B for Black and in position 4: Y for Yellow Digits 2 and 0 correspond respectively to 2 pegs in the correct position and 0 in wrong position. It is also possible to indicate jokers empty cells or unknown indicated by? According to Donald Knuth, and according to the original rules combination of 4 colors among 6 it is possible to find the code in 5 steps or less.

The algorithm to use is:. Otherwise, delete from the set E all the codes that would give the same answer. Give a score to this code equal to the minimum number of possibilities eliminated in E.

Propose one of the codes with the best score as guess preferably a code present in S. Resume in step 3. Mathematically, if the strategy of the code-breaker guessing player is known then there are indeed more or less difficult combinations , but as indicated above , using the optimal strategy of Donald Knuth then no combination is really difficult and all solutions can be found in 5 steps or less.

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Mastermind possible combinations. Share More sharing options Followers 1. Recommended Posts. Function Posted March 10, Posted March 10, edited. Hello On a maths test, I got the following question: The game mastermind starts with forming a secret code, formed by placing 4 coloured pins in a specific order. Thanks Function Edited March 10, by Function. Link to comment Share on other sites More sharing options Posted March 11, I get if I add: the number of possibilities with 4 unique colors the number of possibilities with 2 ordered pins of the same color, with 2 others of unique color the number of possibilities with 2 ordered pins of the same color, with the other 2 pins also an ordered pair.

Is that what the teacher's equation represents? I think this is an error mainly because is greater than The answer I get is doing it 2 different ways: Total arrangements with no restrictions of duplicates -6 arrangements of 4 pins all the same color arrangements of 3 pins of the same color.

Function Posted March 11, Posted March 11, edited. If so, can someone explain it to me? As a matter of fact, I'm afraid my notations aren't very clear? Posted March 12, She's not see my explanation of the symbols above.