Basketball Tracks
Player A, with the basketball, is at the center of the basketball court, and wants to drive towards a spot just before the basket, exactly 40 feet from where he is, on the centerline of the court. Defensive player B, not the brightest of players, always stays exactly 9 feet from him, the line between A and B always parallel with the centerline of the court. In his drive towards that spot, Player A never crosses the track player B makes during this time. In fact, Player A never comes closer than 1 foot from the track player B makes during this time.
What is the minimum distance Player A must travel from the centerline during his drive? The centerline is that unmarked line on the floor passing through the location of both baskets of the court, not that line perpendicular to it as marked in standard courts.
Image credit: Wikipedia Mariusz Swornog
The answer is 4.000.
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1 solution
A solution exists as given. Since with each time A has to go around B's previous position, he has to clear it by at least 1 foot, and since A has to go around B's previous position 4 times, the minimum distance is 4 feet. This is mirrored on the other side of the centerline. Other solutions are possible, but it's not possible to oscillate less than 4 times.
The solution given above have all tracks on a grid with 1 foot spacing. Note that B's track is exactly the same as A's track, but shifted 9 feet to the right.