Please help me understand this.

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Consider a simplified version of Mastermind in which there are three positions and three colors of pegs. There are three possible opening strategies: three of one color (e.g., ), denoted "11 1" here two of one color and one of another (e.g., ), denoted "1 1 2" three different colors (e.g., ), denoted "1 2 3" a) Fill in the table to show the number of codes remaining for each of these opening strategies based on the possible replies the codemaker can give. . 111 112 1 2 3 00 0 000 00 The sum of the numbers in each column should equal the total number of codes, 33 = 27. b) Which strategy leaves the fewest number of remaining codes in the worst case? (This is equivalent to finding the largest number in each column, and then looking for the smallest of these.) c) Which strategy leaves the fewest number of remaining codes on average? (This is equivalen to minimizing the sum of the squares of the numbers in each column. Can you see why?) d) Why is there no row for a response of 0 ? Consider a simplified version of Mastermind in which there are three positions and three colors of pegs. There are three possible opening strategies: three of one color (e.g., ), denoted "11 1" here two of one color and one of another (e.g., ), denoted "1 1 2" three different colors (e.g., ), denoted "1 2 3" a) Fill in the table to show the number of codes remaining for each of these opening strategies based on the possible replies the codemaker can give. . 111 112 1 2 3 00 0 000 00 The sum of the numbers in each column should equal the total number of codes, 33 = 27. b) Which strategy leaves the fewest number of remaining codes in the worst case? (This is equivalent to finding the largest number in each column, and then looking for the smallest of these.) c) Which strategy leaves the fewest number of remaining codes on average? (This is equivalen to minimizing the sum of the squares of the numbers in each column. Can you see why?) d) Why is there no row for a response of 0