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Omni-MATH / Knot is ready to face Gammadorf in a card game. In this game, there is a deck…

Problem

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problem

Knot is ready to face Gammadorf in a card game. In this game, there is a deck with twenty cards numbered from 1 to 20. 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 1,5,10,15,201,5,10,15,20, how many five-card hands of the fifteen remaining cards can Knot draw which always let Knot win (assuming he plays optimally)?
Plain-text mathematical notation (without MathML)
Knot is ready to face Gammadorf in a card game. In this game, there is a deck with twenty cards numbered from 1 to 20. 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 1,5,10,15,20, how many five-card hands of the fifteen remaining cards can Knot draw which always let Knot win (assuming he plays optimally)?
Original LaTeX notation
Knot is ready to face Gammadorf in a card game. In this game, there is a deck with twenty cards numbered from 1 to 20. 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 $1,5,10,15,20$, how many five-card hands of the fifteen remaining cards can Knot draw which always let Knot win (assuming he plays optimally)?

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Source and history

task_id
3207eea1-7bda-526f-b971-b24824d05975
task_key
test--3207eea1-7bda-526f-b971-b24824d05975
task_revision_id
1
config / split
/ test

Official source

initial import