This puzzle is a “Balls on Hills” puzzle. It’s much 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).

Unlike Slitherlink, you do not want to discover a closed loop – fairly, you should discover a curve that partitions the grid into precisely two areas. This is usually a loop, however it will also be a curve that begins and ends on the grid boundary.

Puzzle

Penpa Link

Rules

Curve Rules

1. The resolution 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)

2. The curve travels alongside grid edges (like Slitherlink) inside the grid boundary

3. There is just one curve that matches the constraints

Balls on Hills Clue Rules

1. There is a ball at each quantity. The worth of the quantity signifies the deepest depth the ball might roll right down to. It should roll right down to this depth alongside not less than one path, however it doesn’t should roll right down to this depth alongside each path.

2. Arrows point out path of gravity for the ball.

3. Grid boundary stops the ball as if it had been a part of the curve.

Mechanics of Rolling Balls

1. A ball can roll down any nook.

2. A ball can not roll “up” (towards gravity) a wall or alongside two “horizontal” (perpendicular to gravity) segments in a row (the hill could be too shallow!).

3. Balls don’t intervene with one another (i.e. they’ll go via one another, overlap one another, and many others)

A visible instance could assist:

I’ve highlighted the deepest path a ball can roll down in inexperienced. The instance in purple is an unattainable scenario, because the deepest path for the 1-ball has depth 2.

Extra

This is the second Balls on Hills puzzle. I used to be planning on ready a bit longer to put up this, since I posted the primary yesterday; nonetheless, I spotted 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 will violate uniqueness).

I did not need this to be the case, as a result of I wished reasoning close to the boundary to be tough. 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’m engaged on, however will not put up it for a number of days.

There’s additionally a debate on the identify of the puzzle, since referencing pockets/valleys could be higher suited to the instinct of methods to resolve these (it is best to hopefully see what I imply after giving this a go). Feel free 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).

In common, since this can be a new puzzle kind, any feedback/solutions on the format, guidelines, and many others are welcome!