by John Owen
Published Sunday May 31 2020 (link)
A putting game has a board with eight rectangular holes, like the example (not to scale), but with the holes in a different order.
If you hit your ball (diameter 4cm) through a hole without touching the sides, you score the number of points above that hole. The sum of score and width (in cm) for each hole is 15; there are 2cm gaps between holes.
I know that if I aim at a point on the board, then the ball’s centre will arrive at the board within 12cm of my point of aim, and is equally likely to arrive at any point in that range. Therefore, I aim at the one point that maximises my long-term average score. This point is the centre of a hole and my average score is a whole number.
(a) Which hole do I aim at?
(b) Which two holes are either side of it?