The puzzle considers a single set of 15 checkers (ie. there's no opponent).
Set up the checkers in the standard backgammon starting position.
Then play 3 double rolls of your choice to end up with a 6-prime covering points 7 to 2.
It doesn't matter where the rest of the checkers end up.
The first hint is simply to be show the topics of the other hints. This may
be sufficient to direct your attention without you needing any further help.
The topics are in no particular order. Within a topic, it may be useful to stop after
each step. That may be sufficient to nudge your thinking in a useful direction.
You may like to consider each step within a topic but an alternative is to look at the
first question in each topic. These questions are intended to be as obvious as possible,
such that you may already have considered them.
None of the hints will lead directly to a solution.
Pips
What's the starting pip count, and what is it after the perfect solution (ie. no pips wasted)?
The pip difference limits the combinations of rolls.
The perfect solution uses 52 pips.
The possible sets of rolls are
66, 66, 11
66, 55, 22
66, 44, 33
55, 55, 33
55, 44, 44
and any that are higher.
Pieces
How many pieces are needed for the solution?
Where do they come from?
You must bring four pieces down from the midpoint.
Points
How many points need to be made?
How many points do you need to make per move?
With five points to make and only three moves, you need to make at least one point per move,
or you can have one non-point-maker plus making two and three with the other two moves,
or one non point-maker plus making one point and four points.
Moves
How many moves does it take to make a point?
You can make a point directly in one roll or make it in two by blotting and then covering.