Question

In a game of Incan 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 known, 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.

Answer 1

How high can the score in Incan basketball be?

Consider prime numbers and other numbers that do not factor into either 2 or 5 (e.g., 9) or 3 and 5.

http://primes.utm.edu/lists/small/1000.txt

I hope this helps.

Answer 2

Well, even though I have no experience in this kind of math, i'd say it is not about factoring into prime numbers. To be honest that was actually the first thing I'v though as well. Besides, what is Incan basketball actually?
I suppose it is about numbers written in the form:
n=a*2+b*5, a,b a positive integer or zero.
It can be proven that when there exist i,j for two non negative integers k,l with k > l so that i*k-j*l=1 that only a finite number of natural numbers cannot be written in the form
n=a*k+b*l, a,b positive integers or zero, where at least one of a,b mustn't be zero.

Answer 3

Seriously man, don't try to cheat if you this is for the PROMYS application.