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Math Help - basketball

  1. #1
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    basketball

    In the game of basketball, a points are given for a free throw and b points are given for a field goal, where a and b are positive integers. If a = 2 and b = 5, then it is not possible for a team to score exactly 1 point. Nor is it possible to score exactly 3 points. Are there any other unattainable scores?

    How many unattainable scores are there if a = 3 and b = 5? Is it true for any choice of a and b that there are only finitely many unattainable scores?

    Suppose a and b are unknown, but it is known that neither a nor b is equal to 2 and that there are exactly 65 unattainable scores. Can you determine a and b? Explain.
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  2. #2
    Member SENTINEL4's Avatar
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    For a=2 and b=5 i think there isn't anymore unattainable scores. Having a=2 you can get all even scores (2, 4, 6, 8, ....) and i think you get all odd scores except 1 and 3 by combining 2 and 5.
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  3. #3
    Member SENTINEL4's Avatar
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    For a=3 and b=5 the only scores you can't get is 1, 2, 4, 7 (not 100% sure again).
    Now i will try to take a shot how you can figure it out...

    Let x be the unattainable scores, then x= b+a / b-a (rounding x if necessary)

    NOT SURE FOR THESE ABOVE, TAKE ANOTHER OPINION.
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