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BMAT 2010 · Question 25 · Optimisation

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21 I am playing a card game with three friends. Each of us has two cards which are placed face up on the table. The score for a hand is calculated by adding up the value of the two cards and then doubling the total if the cards are the same suit (denoted by the symbols ♥, ♦, ♣ or ♠). The highest score wins. My two cards are the 2♠ and 7♥. The other hands are: • 4♦ and 7♦ • 5♣ and 8♠ • 2♥ and 9♣ I am the last person to play. I can exchange one of my cards with a card from another hand and I want to finish in the highest position possible.

What will be my score after I exchange cards?