Golfers fondly imagine that every putt can be holed if they apply the correct force and direction to the golf ball, but is this really the case? Given greens with more than one slope, even with perfect smoothness, would it always be possible to make a successful putt? This is an interesting problem for applied mathematics, which could have commercial applications; if golfers knew that a certain putt was impossible to hole, they would adjust their tactics accordingly.
In practice, long putts are often treated as highly unlikely to go into the hole. Golfers realise that the force needed to hole the putt would result in the ball going too far past the hole if it missed. In effect they are worrying about their ability to "hit the target" from a long way off. Tiny variations in direction and proclivity of slopes on the way combine to make the targetting very difficult. But do they make it impossible?
I couldn't find an answer on Google, so this could be a good thesis for somebody. There, it's no longer a googlewhacker.
I'm thinking about a device that could scan a green from the position of the ball and calculate the best shot. I think I've mentioned this before. It could go in the shaft of a putter; might be disallowed, but okay for training. It's a kind of "Dragons' Den" idea, really. [Ed.]