Penultimate FrisbeeMath brain teasers require computations to solve.
The game of penultimate frisbee has two scoring moves: the bungee and the wedgie.
Each type of score is worth an odd prime number of points, with a bungee being worth more than a wedgie. If the largest score that can never be achieved in a game is 95 points (no matter how long the game lasts), how many points is each move worth?
HintIf the two moves are worth p and q, the largest score that can not be
achieved by some combination of bungees and wedgies is p*q-p-q.
AnswerThe bungee is worth 17 points, and the wedgie is worth 7.
The largest score that can not be achieved by some combination of p and q points, with p relatively prime to q, is p*q-p-q = (p-1)*(q-1)-1.
So 96 must be factorable as (p-1)*(q-1), for odd primes p and q.
Since the prime factorization of 96 = 2^5*3, and each of the two
factors must be even, the possible factorizations are:
Only the last factorization yields two factors each of which is one less
than an odd prime, so 17 and 7 must be the two primes we seek.
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