# Puzzle 99: Hochhausblöcke

Hochhausblöcke is a neat skyscraper variant that showed up in the Rätselportal round. They’ve usually been less regular, but from the instructions it was clear that the one on the competition would be an 8×8-grid. I thought there was a good chance of a puzzle without outside clues, and certainly the interactions involved there need more practice, so I tried to construct such a puzzle. I kept running into dead ends, started doubting that they exist at all, and threw the computer at the problem. It turns out that there’s a lot, but they’re rare enough: there’s a good 200000 excluding symmetries, or a little under 1% of all clueless grids you could write down. It should not be unreasonable to find one by hand. Here’s one.

Rules Place numbers from 1 to 4 in each cell so that each row and column of each 4×4-block contains all numbers 1 to 4. Circled numbers are valid skyscraper clues for the adjacent grid (for both adjacent grids in the central corners). Uncircled numbers are not valid skyscraper clues for the adjacent grid (for neither adjacent grid in the central corners).

# Puzzle 98: JaTaHoKu, cryptic

Last JaTaHoKu for now, a JaTaHoKu with cryptic clues. I made a triagonal one, too, but didn’t get around to rendering that yet. Maybe later.

Rules Place numbers from 1 to 6 into some empty cells, such that each row, column and region contains each number exactly once. Clues within the grid are Tapa clues; the numbered cells form a valid Tapa solution with respect to these. Clues along the bottom and right edges are skyscraper clues. Clues along the top and left are Japanese Sums clues, with question marks standing in for unspecified digits. (I.e., 10 would be two question marks.)

Some digits have been replaced by letters. Equal letters correspond to equal digits, different letters to different digits.

# Puzzle 97: JaTaHoKu, cylindrical

Another JaTaHoKu, this time cylindrical.

Rules Place numbers from 1 to 5 into some empty cells, such that each row, column and region contains each number exactly once. Clues within the grid are Tapa clues; the numbered cells form a valid Tapa solution with respect to these. Clues along the bottom and right edges are skyscraper clues. Clues along the top and left are Japanese Sums clues, with question marks standing in for unspecified digits. (I.e., 10 would be two question marks.)

The grid wraps around from top to bottom. Clues along the top act as Japanese Sums clues in order, starting at any group of numbers. Clues along the bottom act as Skyscraper clues, starting at 1. (So for example, a clue ‘1’ is impossible.)

# Puzzle 95: JaTaHoKu

Another JaTaHoKu, this one using the full rule set. It’s probably a bit easier than the first one. Note that the given 4s in the grid are Tapa clues.

Rules Place numbers from 1 to 5 into some empty cells, such that each row, column and region contains each number exactly once. Clues within the grid are Tapa clues; the numbered cells form a valid Tapa solution with respect to these. Clues along the bottom and right edges are skyscraper clues. Clues along the top and left are Japanese Sums clues, with question marks standing in for unspecified digits. (I.e., 10 would be two question marks.)

# Puzzle 94: JaTaHoKu

Another JaTaHoKu I just made, to prove to myself that it’s possible to make accessible JaTaHoKus. You might want to solve this one before the previous one.

Rules Place numbers from 1 to 5 into some empty cells, such that each row, column and region contains each number exactly once. Clues within the grid are Tapa clues; the numbered cells form a valid Tapa solution with respect to these. Clues along the bottom and right edges are skyscraper clues. Clues along the top and left are Japanese Sums clues, with question marks standing in for unspecified digits. (I.e., 10 would be two question marks.)

# Puzzle 93: JaTaHoKu

Here’s a first (Ja)TaHoKu, which I made to prepare for the Logic Masters. Mostly an exercise in the interaction between the Tapa rules and the equal number of cells per row/column/region; that part seems to have potential as a Tapa variation. Would you have thought that even without rooms, the one Tapa clue implies that the mirrored cell has to be shaded?

Rules Place numbers from 1 to 4 into some cells, such that each row, column and region contains each number exactly once. Clues within the grid are Tapa clues; the numbered cells form a valid Tapa solution with respect to these. Clues along the bottom and right edges are skyscraper clues.

# Puzzle 40: Fractional Skyscrapers

Guess I had skyscrapers on my mind after batch-solving the first week of Roland Voigt’s daily puzzles. No, it doesn’t solve as a tightfit skyscraper puzzle.

Rules Place a number between 1 and 6 in each cell (one in each triangle for divided cells) such that each row and each column contains every number from 1 to 6 once. Reading the divided squares as fractions, the numbers in the squares represent the heights of skyscrapers. Clues outside the grid indicate the number of skyscrapers that can be seen when looking into the corresponding row or column. Skyscrapers block the view to any other skyscrapers of smaller or equal height behind them.

Example

# Puzzle 18: Afternoon Skyscrapers

Another practice puzzle for the GP.

Rules Fill the grid with numbers from 1 to 6 such that every row and column contains all numbers. The numbers represent skyscrapers of the given height. There is a gray shadow at the south edge of a cell if some skyscraper further south in that column would throw a shadow onto the roof of the skyscraper in that cell, with the sun shining at a 45º angle. Similarly, a shadow on the west edge corresponds to sunshine from the west.

Or see the instruction booklet.