Consider a cue ball, an object ball, and a hole lined up perfectly. Let the cue ball be an arbitrary fixed distance from the hole. Where in between the cue and hole should the object ball be for the most difficult shot? If the object ball is just on the edge of the hole, the shot is easy: any contact with the ball will knock it in (amount of error is the angular width of the object ball). If the object ball is frozen against the cue ball, but lined up, again the shot is easy (almost 180 degrees of error). There must be some point in the middle where the shot is most difficult.
For a single object ball and a cue ball in hand which must be shot out of the kitchen, what is the surface of difficulty throughout the possible positions of the object ball?
For all possible positions of the object ball, where in the kitchen is the optimal placement for the easiest shot?
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