Bowling Game Second Story

After examining the ObjectMentorBowlingGame score and discussing the lack of a frame object of any sort (and the desirability or not of having one) a couple of programmers turned to the question of how this solution compares to one that could get be implemented in a pure ProceduralLanguage -- CobolLanguage, to use a devilish example. And thus a second story for the BowlingGame was born.

I would like to know, based on my current score and place in the game, what's the fewest number of throws I need to reach a specified score -- if I can at all?

Example: I've had 7 throws, my score is 42 (I don't bowl much), what's the fewest throws I need to reach 100, if I can at all?

Example 2: I'm on the ninth frame. My opponent just finished with a 286, my score is 210. How many throws do I need to beat her? Can it even be done?

-- StevenNewton

Or, given 7 frames, and a score of 42, what is my maximum possible score for this game?

Good questions all. I like 'em, I like 'em. An experienced bowler can probably answer these in his/her head. But the problem is to get a computer to answer them.