Broken Sign Blog
#055: Moon and Sun (Dance / Nested)
11 November 2022My first doppel! I constructed this for Logic Showcase #40 on Puzzlers Club, “Single-Genre Stacking” and ended up reaching second place. The prompt was to make puzzles that have at least two solutions under some constraints, such as Twopa puzzles. I had two ideas for how to interpret the prompt for a loop puzzle and decided to go for the ultimate flex and construct a doppel for both options.
I’m actually really excited about the Dance variant in particular. I’m sure you’ve noticed that I’ve been exploring tons of loop variants with Rail Pool, and I still have a list of ideas to try in the future. One idea that has been sitting on that list for a long time is to make a Rail Pool with two loops, and some constraint on how those loops should behave. But I’ve been struggling to come up with any good constraints that naturally enforce both loops to be equally important (and not create some big uniqueness issues). For example, the Nested variant used here would probably just lead to a very small inner loop in Rail Pool, because there’s by default no requirement for each loop to visit every region.
For the logic showcase, I decided to go with a loop genre that naturally comes with its own duality, Moon or Sun. It makes some amount of sense to look for two solutions which have moons and suns swapped in each region. However, the Nested variant seems a little too restrictive to make super interesting puzzles and so I wanted to allow crossing. I think the Dance rules I ended up on (exactly one crossing in each region) are just the right amount of constraint and flexibility, and they’re quite nice thematically. But most of all, they should generalise very well to all sorts of loop genres. For genres without regions like Masyu or Balance Loop, the condition could be replaced with having to cross once after each clue, for example. So I’m really looking forward to experimenting with this variant in other genres in the future.
A note on Penpa: it might be helpful to use different colours for the two loops. But you’ll have to redraw everything in green once you’re done to get the answer check.
Rules: Draw a non-intersecting loop through the centres of some cells which passes through each region exactly once. Within a region, the loop must pass through all moons and no suns, or all suns and no moons. A region containing only suns or only moons must have its clues passed through. The loop may not pass through the same type of clue in two consecutively used regions.
Variant: Moon and Sun — Draw two loops instead of one, each satisfying the rules above. Every clue must be visited by some loop.
Dance — The loops cross each other at right angles exactly once in each region. They cannot cross themselves or otherwise overlap each other.
Nested — One loop is completely contained inside the other. The loops cannot touch or cross themselves or each other.