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by Fred Schneider

by Fred Schneider

Here's another hybrid puzzle. In a sense, each solution is both a valid Nurikabe and a valid Fillomino solution.

All given numbers clues in the puzzle are Fillomino-style clues. Each bold number is also a Nurikabe clue (referring to an "island" of that many squares).

There's an additional dimension to the puzzle. Each island of size n needs to be filled with numbers from 1 to n, one square each. This aspect of the puzzle is similar to the Nurikabe Sudoku puzzle I published last year.

Incidentally, I was going to call this Nuri-Fill originally, but I decided it sounded too much like a cough medicine or something. :)

Hopefully, the sample puzzle sheds some light.. Note how there's only one possible place for 2-square in the 3-island given the 5 clue in the 4th column.

On to the puzzles! Any feedback is welcome. These two are on the easier side and I think the logic required to solve them has a nice push-and-pull between the two puzzle types.

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Puzzle 2 (13x12, Medium):

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This is another variation on Nikoli's Heyawake puzzle and assumes familiarity with those rules.

I wanted to create puzzles that incorporated some simple equations/relations, venturing out beyond the single operator logic used in puzzles like Ken-Ken and Futoshiki.

For instance,

The name is a portmanteau of algebra and Heyawake. The word Heyawake always sounded vaguely Arabic to me so it's an apt name I think.

Any feedback welcome. Admittedly, these are on the harder side, especially #4.

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Thanks to

This is a new 3-d puzzle type based on an earlier type of mine called Dervish Packing.

This puzzle consists of several square grids of the the same dimension that together make up a cube. Future puzzles could be rectangular solids as well.

The solution requires that each block in the solid have a letter with the following constraints:

- Each letter refers to a different polyomino* which is 2-fold rotationally symmetric (meaning if you rotate the shape 180 degrees about it's center, it appears the same as the original). As polyominoes are planar, in the Z axis, there's a constant width of 1.
- No two different letters map to the same polyomino.
- There are no hidden shapes. So, each polyomino must be identified on the board by one or more of its blocks via a letter clue.
- Different polyominoes of the same letter may have common vertices or edges but NOT faces.

Here's a sample point to illustrate the rules. Note below that the leftmost grid is the top floor of the cube, the middle is the middle and the rightmost is the bottom floor.

(The greyed blocks in the grids are just for illustration. They just indicate the shapes that ended up being placed vertically in the puzzle.)

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**Any feedback is welcome. Thanks for playing!**

Here's a somewhat larger puzzle of a type I came up with late last year. The original post (along with the rules and a walkthrough) is here.

I think this is my first repeat puzzle on this blog. I got some nice feedback on this type last year so I hope you enjoy it.

One hint in solving this puzzle (if you get stuck) is to remember that all the whitespace must be connected and this has implications for the edges of the puzzle.

Any feedback is welcome.

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**Puzzle 4 (16x16, Medium-Hard):** (Answer)

This is a variation of Nikoli's Masyu puzzle and the explanation below assumes familiarity with it. Like normal Masyu, each puzzle has a unique solution in the form of a loop which does not intersect itself and satisfies all of its constraints (in the form of "pearls").

I wanted to create a version that makes uses of diagonals as well, which introduces two new clues.

Having line segments that could arbitarily move in 8 directions would be unwieldy. So, there's a 5th type of clue that works as a connector or bridge between the diagonal and orthogonal and (in its behavior) is like a hybrid of black and white clues.

Here is the key and a bit more detail on how the clues can behave:

Any feedback is welcome. On to the puzzles!

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Puzzle 2 (12x12, Medium):

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Special thanks to

This is a variation of Nikoli's Heyawake puzzle where numbered squares indicate how many edges of the square

The colored squares follow the rules of Heyawake: at no point in the puzzle can a single file of adjacent blank squares span more than two boxes and all the white squares (the water) must be connected orthogonally.

Any feedback is welcome. (In particular, I'd be curious if anyone has seen this variation before.)

Incidentally, going forward, I'll be using site.google.com to store puzzle images. Too many problems with my band's domain (and its ultra-flaky provider www.hostonce.com).

It's on the newstand. Please check it out. :)

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On a different positive front, my band Bosola's debut EP "RE" got a nice review here.

Tandem puzzles are pairs (trios, etc.) of puzzles that are related to each other by shared letter clues. The cool thing about this idea is that the two puzzles don't have to be of the same type. The idea is to alternate between puzzles making headway on one and using those solved clues to make progress with the other and vice-versa until all of the components are solved.

Within each pair, all clues of a certain letter correspond to the same number. More than one letter however may refer to the same number and it's not necessary for a specific letter to appear in both puzzles of a pair.

The number value of letters can be determined by considering the constraints those letters are subject to in the different puzzles.

There is a no sample for this type but here's a couple of observations about the first puzzle:

In the Sudoku half of the first puzzle, one could see that D, E, and F in column 3 must have different numerical values and that B, A, and D are different values because they occupy the same box in the upper left. In the Nurikabe half of the first puzzle, one can deduce the value of B, E then A and then replace those letters with their values in both puzzles, and then make progress with the Sudoku side.

These puzzles are solvable by logic alone and have each has a unique solution pair.

Any feedback is welcome. Enjoy!

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I don't know if any readers of this blog noticed my name in Games magazine this month (May's issue is on the newsstand until the 24th). If not, I got an original puzzle published called Serpent Factors. First time published, yay! In August, its sister, Factor Flowers will be published. These are the first two puzzles sets that I wrote back in May of last year, "Flowers" being the first.

If anyone happened to work through the puzzles in May magazine, they likely noticed some of the puzzles don't have a unique solution. Unfortunately, I noticed the problem after they were submitted and when I contacted them they had already gone to press. They also said their tester hadn't noticed the lack of uniqueness in some of them.

So, the first three puzzles are scrubbed versions of the problematic published puzzles. Puzzles 4 and 5 weren't published in the article. These fall on the hard side so hopefully the sample and tips will shed some light on how to do these.

Rules: Serpent Factors

1) Each number is the head of a serpent with one or more segments emanating from it. (The exceptions are zero squares which have no "body").

2) Each segment can extend in a straight line horizontally, vertically or diagonally. If it's connected to another segment it must not extend in the same or opposite direction.

3) The "lengths" of the segments must multiply to the number in the head. The length of the segment is defined as the number of squares it touches (i.e. if a segment touches halves of two squares, it's "length" is 2).

4) Each segment must have a length which is a prime factor of the number (for example: 20's prime factorization is: 2*2*5 so the snake must have segments of lengths 2, 2, and 5 in some order and orientation). Exception: When the number in the square is 1, the snake will have a single segment of length 1.

5) Each clear, non-numbered square requires exactly one serpent passing through it.

Tips:

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Puzzle 3 (10x10, Hard): (Answer)

As it sounds, this combination of the old favorite Battleships with the more recent Nikoli puzzle Heyawake. This idea was inspired by Thomas Snyder's great book: Battleship Sudoku.

The solution must be a valid Heyawake solution while placing each of the ships specified so they do not touch each other, even diagonally.

Unlike regular Battleship puzzles, in this variation, the ships are placed

Like Battleship, there are numeric clues outside the grid. Because the ships are placed diagonally, the clues refer to the number of segments in the diagonals (which wraparound toroidially). The arrows below indicate the two sets of diagonals for the same small sample (along with the segment counts outside the grid for each diagonal):

One more thing: due to the primitive tools at my disposal, you'll notice none of the "ships" have a head or tail. So, none of the puzzles have ship segments placed in them as clues.

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Puzzle 2 (9x9, Easy to Medium): (Answer)

Puzzle 3 (10x10, Medium): (Answer)