Henry Ernest Dudeney/Puzzles and Curious Problems/316 - Queer Golf/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $316$

A certain links had nine holes, $300$, $250$, $200$, $325$, $275$, $350$, $225$, $375$, and $400$ yards apart.

If a man could always strike the ball in a perfectly straight line and send it exactly one of two distances,

so that it would either go towards the hole, pass over it, or drop into it,

what would those two distances be that would carry him in the least number of strokes round the whole course?

Two very good distances are $125$ and $75$, which carry you round in $28$ strokes,

but this is not the correct answer.

The two best distances are:

$100$ yards (known as "the appproach")

and:

$125$ yards (known as "the drive").

Hence:

Hole $1$ can be reached in $3$ approaches

Hole $2$ can be reached in $2$ drives

Hole $3$ can be reached in $2$ approaches

Hole $4$ can be reached in $2$ approaches and $1$ drive

Hole $5$ can be reached in $3$ drives and $1$ backward approach

Hole $6$ can be reached in $2$ drives and $1$ approach

Hole $7$ can be reached in $1$ drive and $3$ approaches

Hole $8$ can be reached in $3$ drives

Hole $9$ can be reached in $4$ approaches

which is $26$ strokes in all.