Friday, June 6, 2008

Some more puzzles

30. 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, and 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
• Black keypeg = one of B's pegs is the correct color and in the correct position
• White keypeg = one of the B's pegs is the correct color but in the wrong position
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 A's arrangement?

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