This puzzle is a “Balls on Hills” puzzle. It is just like puzzles like Slitherlink in that your aim is to discover a curve given some clues. The instinct behind this puzzle is balls rolling down hills into valleys (pockets).
Not like Slitherlink, you do not want to discover a closed loop – slightly, you should discover a curve that partitions the grid into precisely two areas. This could be a loop, nevertheless it may also be a curve that begins and ends on the grid boundary.
The answer is a single, non-self-intersecting curve that partitions the grid into two zones (whether or not by looping or beginning and ending on the grid boundary)
The curve travels alongside grid edges (like Slitherlink) throughout the grid boundary
There is just one curve that matches the constraints
Balls on Hills Clue Guidelines
There’s a ball at each quantity. The worth of the quantity signifies the deepest depth the ball may roll right down to. It should roll right down to this depth alongside at the least one path, nevertheless it doesn’t must roll right down to this depth alongside each path.
Arrows point out course of gravity for the ball.
Grid boundary stops the ball as if it had been a part of the curve.
Mechanics of Rolling Balls
A ball can roll down any nook.
A ball can’t roll “up” (in opposition to gravity) a wall or alongside two “horizontal” (perpendicular to gravity) segments in a row (the hill could be too shallow!).
Balls don’t intervene with one another (i.e. they will move via one another, overlap one another, and so on)
A visible instance might assist:
I’ve highlighted the deepest path a ball can roll down in inexperienced. The instance in crimson is an unattainable state of affairs, because the deepest path for the 1-ball has depth 2.
That is the second Balls on Hills puzzle. I used to be planning on ready a bit longer to publish this, since I posted the primary yesterday; nevertheless, I noticed one thing a tad irritating: by the previous guidelines (make a loop as an alternative of “partition into two”), you would by no means contact the boundary (it might violate uniqueness).
I did not need this to be the case, as a result of I needed reasoning close to the boundary to be troublesome. I’ve modified the rule to “partition into two”, which I believe retains the spirit of the puzzle. By posting this so quickly after the primary puzzle, I hope it serves to “canonize” this rule change 😉 I do have one other Balls on Hills that I am engaged on, however will not publish it for just a few days.
There’s additionally a debate on the identify of the puzzle, since referencing pockets/valleys could be higher suited to the instinct of tips on how to clear up these (you must hopefully see what I imply after giving this a go). Be at liberty to counsel a reputation. I’ve stored it as “Balls on Hills” for now as a result of each phrases finish in the identical consonant cluster (lls).
On the whole, since it is a new puzzle sort, any feedback/strategies on the format, guidelines, and so on are welcome!