Monthly Archives: June 2016

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.)

hochhausblock-max hochhausblock-min

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 106: Pentowords

We’re reaching the end of the series of LM practice puzzles. Pentowords is an interesting new (to me) type that was also on the mixed round. The one on the contest was built around a letter packing argument (though I only half saw that while solving), this one is quite different.


Rules Split the grid into the twelve different pentominos, and write each of the given words into one of the pentominos, left to right then top to bottom. Same letters must not touch by edge. Some letters are already given.

Puzzle 104: Keller, Japanese Sums+Dotted Snake

Last of the Kellers, and the hardest. You really can’t say I wasn’t prepared.


Rules The left grid is a Japanese Sums puzzle, digits 1-8. Place digits in some cells, so that they don’t repeat in rows or columns. Clues give the sums of blocks of adjacent digits in order. The right grid is a Dotted Snake: Draw a snake of any length that occupies full cells and doesn’t touch itself, not even diagonally. Numbering the snake cells from head to tail, put a dot in every third cell, starting with the third. Clues indicated the number of dotted snake cells in the corresponding row or column.

The grids interact: There must be a digit under every snake cell, and that digit must be divisible by three if and only if the corresponding snake cell is dotted.

Puzzle 103: Keller, Fences+Dominoes

Next Keller puzzle. Some of the logic may have been lost in completing the domino part for this one. I find the restrictions that the compatible domino tiling imposes on the loop to be quite interesting in this type, the interaction with the domino puzzle as such less so.


Rules The left grid is a domino dissection puzzle. Divide the grid into 2×1-areas such that each domino occurs exactly once. The right grid is a standard fences/slitherlink.

The grids interact: Superimposed over the solved domino grid, the fence can’t bisect a domino.

Puzzle 102: Trinudo

Another break, this time for the series of Kellers. This one didn’t come out quite the way I wanted and could use a bit of polishing, but…


Rules Split the grid into areas of size 1, 2, 3 such that areas of equal size don’t touch along an edge, and such that any given number is contained in an area of that size. (I.e., Fillomino with areas of size at most 3.)

Puzzle 101: Keller, Sternenhimmel+Magnets

Another practice puzzle for the Keller round. This one has a wart, I messed up the sign on the break-in, and don’t see a nice way to fix it. This will have to do. I don’t remember whether it’s actually difficult, beyond the awkwardness of the type.

EDIT: Fixed an ambiguity, thanks uvo.


Rules The left grid is a Sternenhimmel. Place some stars in empty cells, such that every arrow points at at least one star, and such that every star is pointed at by at least one arrow. Clues outside the grid indicate the number of stars in the row or column. The right grid is a Magnets grid. Place + and – in some cells, such that every 2×1-plate is either completely empty/shaded (neutral), or has one + and one – (charged). Same signs can’t be adjacent.

The grids interact: Stars may only be placed over charged plates. Arrows over charged cells are rotated (90˚ clockwise for +, counterclockwise for -).

Puzzle 100: Keller, Mosaik+Labyrinth

Here’s a puzzle for one of the types on the Keller round, with superimposed puzzles.


Rules Solve the left grid as a Mosaik. That is, shade some cells, such that each number indicates the number of shaded cells in the surrounding cells, including the cell itself (so, 9 is the maximum clue). Solve the right grid as a Magic Labyrinth with digits from 1 to 3. That is, place digits 1, 2, 3 in some cells such that every row and column contains each digit exactly once, and walking along the labyrinth from outside to inside, you visit digits in the repeating order 1,2,3,1,2,…, starting with 1.

The two puzzles interact: Whenever a Mosaik clue is shaded, copy that clue to the Labyrinth in the corresponding position.

Puzzle 93b: Regular Tapa

I thought the underlying “regular” Tapa from the JaTaHoKu I published earlier was worthy of a dedicated post. Is there a name around for this variant?

While resolving this one will require a few case distinctions, it does have a reasonable break-in, and is quite doable if you choose the right spots. It’s possible that prescribing the number of shaded cells is not necessary, give it a try with three shaded cells per row/column.


Rules Solve as a regular Tapa. Additionally, there must be exactly four shaded cells in every row and column.