Broken Sign Blog
#160: Twisted Tower
29 November 2024Last weekend, the German puzzle community met up for a puzzle weekend in Kassel and I made this puzzle as a team event for the occasion.
(The tower in the photo was assembled randomly and does not reflect the actual solution.)
I’ll talk about the construction process and the event in the next post, so as not to clutter this one. As you can see above, for the event I built components to assemble an actual tower in 3D, but it’s also possible to solve the puzzle (mostly) in Penpa or on paper, as the test solvers had to do. I would generally recommend solving this puzzle on paper instead of digitally. Without being able to physically align the floors of the tower, you’ll have to visualise the connections in your head.
- For solving on paper, you only need the PDF version below. Note that there are two versions of the cylinder grids in the PDF. The regular ones are what I used to assemble the 3D tower, and you can do the same if you can get your hands on some suitable cylinders. This is the intended way to experience the puzzle, but is probably not an option for most solvers.
- Alternatively, there’s another version where the cylinder grids have been duplicated horizontally. This makes it easier to solve the puzzle as flat paper strips, because you can copy the solution over and align subsequent layers more easily. You’ll still need to visualise the connections from the circles to the cylinders.
- If you want to solve the cylindrical grids digitally, there is a Penpa link below. The cylinder grids can’t be represented in Penpa, so you’ll have to solve them in the PDF or on a screenshot (or solve only those on paper). If your browser complains about the URL being too long, go to Penpa directly, click the “Load” button and paste the URL there.
The PDF also contains an example puzzle, whose cylinder portion you can also solve digitally. This example is pretty spicy, but should be an interesting puzzle in itself, which contains some logic that I had to avoid in the main puzzle due to difficulty concerns.
Note that there’s an important rule difference between the example and main puzzle: in the example, the floors must not be flipped upside down, whereas this is allowed (and the orientation to be determined by the solver) in the main puzzle. This is because I wanted to keep the extra degree of freedom as a surprise for the live event.
Rules: This puzzle consists of the following layers:
- A large circular grid with a hole in the centre (the tower garden).
- Six rectangular grids, each on the outside of a cylinder, i.e. the short sides are connected to each other (the floors).
- A small circular grid (the observation deck).
These layers are assembled into a tower by stacking the six floors in the centre of the tower garden and placing the observation deck on top. The order of the floors, the relative rotation of consecutive layers, as well as which side of each floor is up, are all for the solver to determine.
On the assembled tower, draw a path from the entrance at the edge of the tower garden to the centre of the observation deck, which follows the rules of each grid it passes through. The path generally travels between the centres of cells which share an edge. The only exception is the observation deck, where the path travels along grid edges (therefore, the observation deck will appear to be misaligned by half a cell with the layer below). The path cannot cross itself or otherwise revisit a cell (or vertex), unless a layer’s rules explicitly allow this.
Once the path visits layer N for the first time, it can no longer return to layer N–2 (this includes the tower garden and observation deck).
The individual layers obey the following rules:
Tower garden: Remaze
The path visits every circle. At each circle (and only there) a single dead end branches off from the main path. The branches cannot leave this layer. The endpoints of all branches are marked with an X. Each cell is used either by the main path or by one of the branches.
Kaisu
The path visits every cell. The path’s Nth visit to a region must pass through exactly 0 or N circles.
Meandering Words (Visits)
The path cannot visit cells with black squares. Write a letter into each cell visited by the path. Identical letters cannot appear in diagonally or orthogonally adjacent cells. When reading the letters (forward) along the path, each visit to this floor spells out one word from the given list, such that each word is used exactly once. Some letters are given (and must be visited). Given M and W must be rotated correctly in the solution.
Elbschiffer
The path visits every circle. It turns right on circles containing X and left on circles containing +. Not all possible circles are given.
Icebarn
The path may intersect itself on ice. The path cannot turn on ice. The path visits every patch of ice at least once. The path passes through each arrow in the indicated direction. (Note: as opposed to the example puzzle, there may be unvisited cells, both ice and regular cells. It is sufficient for one cell per connected ice patch to be visited.)
Silo
Each visit to this floor is split into sections of exactly four cells, forming tetrominoes. The path passes through every letter, indicating the shape of the tetromino covering this cell. During a single visit, tetrominoes cannot repeat, treating rotations and reflections as the same. (Note: as opposed to the example puzzle, there may be tetrominoes not passing through any clue.)
Oriental House
The path passes through every cell. When the path passes through an arrow, the current visit to its region must have entered and/or must exit the region in the indicated direction.
Observation deck: Irregular Slitherlink
The path travels along gridlines. Numbers indicate how many of the gridline segments around the clue are used by the path. (Note: not all cells have the same number of gridline segments around them.)