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Math Help - Card Game

  1. #1
    Junior Member
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    Card Game

    Jon and Paul are playing a card game. Jon shuffles a set of 14 cards, numbered consecutively from 1 to 14. He deals them, giving seven to Paul and seven to himself. In this game, a persons score is the total of the numbers on the seven cards received. Jon wins if his score is greater than Paul's score. The number of possible winning scores available is:
    a) 24
    b) 25
    c) 52
    d) 53
    e) 105

    i think the answer is 24, but i dont know why :S
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  2. #2
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    Jello, foreverbrokenpromises!

    Jon and Paul are playing a card game.
    Jon shuffles a set of 14 cards, numbered consecutively from 1 to 14.
    He deals them, giving seven to Paul and seven to himself.
    A player's score is the total of the numbers on the seven cards received.
    Jon wins if his score is greater than Paul's score.

    The number of possible winning scores available is:
    . . (a)\;24 \qquad (b)\;25 \qquad (c)\;52 \qquad (d)\;53 \qquad(e)\;105

    The total number of points available is: . 1 + 2 + 3 + \hdots + 14 \:=\:105

    To win, Jon must have a minimum of 53 points.

    His maximum is the top seven cards: .  8 + 9 + 10 + \hdots + 14 \:=\:77 points.

    \text{The winning scores are: }\;\underbrace{53,\:54,\:55,\:\hdots \:77}_{\text{ 25 scores}}

    . . There are 25 winning scores . . . answer (b).

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