Mastermind Problem (S461)
From: William Wu of U.C.Berkeley on 8/24/2005
This is the logic game of Mastermind. If you haven't played it before, here's how it works. There is a board that is sectioned off into many rows, each row having four slots in which pegs can be inserted. There are six different colors of pegs: green, red, yellow, brown, dark-blue, light-blue. There are two players, A and B. First, A makes up some arrangement of four pegs along a row, the colors and ordering of which are his or her choice. Then B spends the rest of the game trying to guess what A's arrangement is. For every guess that B makes, A will respond by putting some black and/or white pegs right next to A's guess; the black and white pegs are interpreted as follows:
= one of B's pegs is the correct color
So if B manages to guess all four colors
and positions correctly, A will respond with four black keypegs, and the
game is over. The goal is to determine A's secret arrangement in the minimum
number of guesses. Below, we see a completed game of Mastermind. Apparently
the player was able to determine A's arrangement by using only four guesses.
What's is A's arrangement?