Problem:
Knot is ready to face Gammadorf in a card game. In this game, there is a deck with twenty cards numbered from to . Each player starts with a five card hand drawn from this deck. In each round, Gammadorf plays a card in his hand, then Knot plays a card in his hand. Whoever played a card with greater value gets a point. At the end of five rounds, the player with the most points wins. If Gammadorf starts with a hand of , how many five-card hands of the fifteen remaining cards can Knot draw which always let Knot win (assuming he plays optimally)?
Solution
Solution:
Answer:
Knot can only lose if all of his cards are lower than ; if not he can win by playing the lowest card that beats Gammadorf's card, or if this is not possible, his lowest card, each turn. There are losing hands, so he has possible winning hands.
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