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.