Mastermind is a game in which you have to guess a hidden code made of 4 “color p
Mastermind is a game in which you have to guess a hidden code made of 4 “color pegs” (a tuple), from a set of 7 colors {R,G,B,Y,W,K,O}. The code maker responds to your guess with smaller “key pegs,” which are black or white (a multiset) and indicate exact or color matches with the code. (More precise definition below.)
Your assignment:
Read this guide and return to it, because I’ll update with pointers to answers with comment.
#1 Is a problem with a danger of overcounting codes with repeated colors, so I give three ways to count.
Each has an explanation from chatGPT that is often wrong, as it learns when I tell it to “Check that by brute force.” That will tell you the target number.
Make your answer self-contained by briefly restating the problem. E.g., “A guess of RRGW got a response of one black, one white key pegs. Let’s count how many codes are consistent with that response.”
question #1. You are playing Mastermind by making a guess that is a 4-tuple drawn from a set of 7 color pegs, {R,B,G,Y,W,K,O} (order matters, repeats allowed). The codemaker responds with a multiset 0 to 4 black or white key pegs (order doesn’t matter; repeats allowed). Each b indicates some guess peg matches the code in position and color; w indicates some guess peg has a right color in the wrong position. (A more precise statement of the rules is in CW#30.)
You want to know how many codes are consistent with the response to your guess, because that is the first step to narrowing this down to one code.
Here is your guess and the response:
RRRYww
https://chat.openai.com/share/ea81a6de-48cd-442f-8…
question 2: You are playing Mastermind by making a guess that is a 4-tuple drawn from a set of 7 color pegs, {R,B,G,Y,W,K,O} (order matters, repeats allowed). The codemaker responds with a multiset 0 to 4 black or white key pegs (order doesn’t matter; repeats allowed). Each b indicates some guess peg matches the code in position and color; w indicates some guess peg has a right color in the wrong position. (A more precise statement of the rules is in CW#30.)
You want to know how many codes are consistent with the response to your guess, because that is the first step to narrowing this down to one code.
Here is your guess and the response:
RGBKw: https://chat.openai.com/share/aed9a55d-12d8-402a-9…
Please restate the guess and response to make your answer self-contained. You are encouraged to find different solutions from existing answers, or present it in a different way (with diagrams, to a bright middle schooler, as briefly as possible, …) or diagnose what the linked ChatGPT transcript gets right or wrong. (It’s “check by brute force” does report the right number, though its explanation is often wrong.)