# Puzzle 120: Hochhausblöcke

Some more Hochhausblöcke. In other news, the 10×10×10 series on croco-puzzle continues, and I submitted a few puzzles to the excellent puzzlepicnic, including a Fences puzzle where I’m curious to know if people find the intended break-in, and a Yajilin.

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).

# Puzzles 107, 108: Hochhausblöcke

To make it a full two weeks of post-LM posts, here are two more Hochhausblöcke. One with the maximal number of givens, one with the minimal number. (There are some more of each, but these are the nicer ones. The minimal one requires a well-placed deep case distinction, or I do at least.)

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 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).