Problem 52110. Pick the die most likely to win
After discussing Rock, Paper, Scissors, Lizard, Spock in The Simpsons and their Mathematical Secrets, Simon Singh writes that investor Warren Buffett will challenge people to beat him in a game of dice. He presents three dice and asks the other person to choose one. Then he chooses one, and they roll together. The person with the highest roll wins.
With standard dice that have one to six pips on their sides, no one has an advantage. However, Mr. Buffett’s dice are different: Although the sum of the numbers on the faces of one die equals the sums for the other dice, the numbers on one die differ from the numbers on the other dice.
For example, suppose die A has 1, 1, 6, 6, 8, and 8; die B has 3, 3, 5, 5, 7, and 7; and die C has 2, 2, 4, 4, 9, and 9. If the first person chooses die A, then Warren Buffett will choose die C to increase his chances of winning. Write a function that choose the die most likely to win, given the other person’s choice. The input is a matrix with the numbers on the faces of each die in the rows and an index of the die (i.e., row) that the other person chose.
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