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This is a “Twisted Tuesday” puzzle variation.

Theme: Inverted Clues

Rules: Variation of Cross the Streams rules. The clues in this puzzle are inverted. They indicate the WHITE (unshaded) areas, not the black areas as in other Cross the Streams. The shaded cells must still obey the regular rules (connectivity, no 2×2 squares).

Answer String: Enter the length in cells of each of the black segments from top to bottom for the marked columns, going in order from A to B to C to D and separating each entry with a comma.

Time Standards (highlight to view): Grandmaster = 2:15, Master = 3:30, Expert = 7:00

Solution: PDF

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to shift between shading mode and the linex mode where left click+drag draws lines and right click marks X’s)

This is a “Franken-Friday” puzzle variation.

Theme: Prime Time

Rules: Standard Cave rules, except the grid is hexagonal.

Answer String: Enter the length in cells of each of the internal cave segments following the arrows for the marked rows, starting at the top. Separate each row’s entry with a comma.

Time Standards (highlight to view): Grandmaster = 6:00, Master = 8:30, Expert = 17:00

Solution: PDF

Note: Follow this link for other classic Caves. If you are new to this puzzle type, here are our easiest Cave Puzzles to get started on.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between “big” sudoku and “small” number entry modes.)

This is a “Twisted Tuesday” puzzle variation.

Theme: Cage symmetry and repeated clue values

Rules: Variation of standard TomTom rules. The indicated range [1-6] is larger than usual for a 4 x 4 puzzle. Some cells containing slashes require two digits to be placed. These cells should be treated as fractional values (top value over bottom value) for the purposes of solving the puzzle.

Answer String: Enter the 3rd row from left to right, followed by a comma, followed by the 4th row from left to right. (Note: for the cells with slashes, enter the top before the bottom.)

Time Standards (highlight to view): Grandmaster = 2:30, Master = 3:30, Expert = 7:00

Solution: PDF

Note: Follow this link for other classic TomTom. If you are new to this puzzle type, here are our easiest TomTom to get started on.

PDF

or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s)

This is a “Franken-Friday” puzzle variation.

Theme: Half Truths

Rules: Variation of Masyu rules. Half of the circles are lying; a lying white circle is actually a black circle and a lying black circle is actually a white circle. The loop must alternate between true circles and lying circles (T-L-T-L-…).

Answer String: Enter the length in cells of the horizontal loop segments from left to right in the marked rows, starting at the top. If the loop only has vertical segments in the marked row, enter 0. Separate each row’s entry with a comma.

Time Standards (highlight to view): Grandmaster = 5:30, Master = 10:00, Expert = 20:00

Solution: PDF

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing, a number entry mode, and shading for this variation.)

Theme: Visual and logical

Rules: Variation of standard Fillomino rules. All polyominoes of same size besides 4 cannot touch. But all tetrominoes — polyominoes of size 4 — must be connected as in a LITS puzzle. All “4” clues have been replaced by letters indicating which tetromino type they belong to.

Answer String: For each cell in the marked rows, enter the area of the polyomino it belongs to. For the tetrominoes, instead of numbers use capital letters (L, I, T, S) in the appropriate cells. Start with the 6th row, followed by a comma, followed by the 14th row.

Time Standards (highlight to view): Grandmaster = 7:00, Master = 10:30, Expert = 21:00

Solution: PDF

Note: Follow this link for other classic Fillomino and this link for more variations on Fillomino puzzles. If you are new to this puzzle type, here are our easiest Fillomino puzzles to get started on.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a Shading mode and a composite Yajilin mode where left click inside cell shades square, left click + drag draws line segment, right click inside cell adds dot, and right click on cell edge adds an x.)

This is a “Franken-Friday” puzzle variation.

Theme: Mostly logical; after solving, did you notice the message in the top few rows?

Rules: Standard Cross the Streams rules. Also, the shaded region must be able to be split into tetrominoes to form a valid LITS solution.

Answer String: Enter the length in cells of each of the black segments from top to bottom for the marked columns, going in order from A to B to C to D and separating each entry with a comma.

Time Standards (highlight to view): Grandmaster = 4:00, Master = 7:30, Expert = 15:00

Solution: PDF

PDF

or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s)

This is a bonus “Twisted Tuesday” puzzle variation.

Theme: None?

Rules: Standard Double Back rules (originally from MellowMelon). In short: draw a single loop that enters and exits every cell exactly once, and enters and exits every region exactly twice.

Answer String: Enter the length in cells of the horizontal loop segments from left to right in the marked rows, starting at the top. If the loop only has vertical segments in the marked row, enter 0. Separate each row’s entry with a comma.

Time Standards (highlight to view): Grandmaster = 2:15, Master = 3:30, Expert = 7:00

Solution: PDF

Here are the final puzzles from the US Sudoku Qualifying Test that I wrote. Both are less common types. Tomorrow will finally bring some new puzzles, and I hope some surprises too.

The first of this set, a “Seek-and-Spell” variant, is a style that took on a life of its own on this website a few months ago as more and more constructors kept submitting it. I wanted a very United States sort of puzzle somewhere on this test and found a good letter set to get 5 states into this grid. I wanted OHIO from the start as an easy Seek-and-Spell rule placement. But the value of states like MONTANA and INDIANA became clear during construction. This may have been the only case on the test where some non-sudoku logic puzzling skill would really accelerate the solve as the Seek-and-Spell placements are quite limited and getting them fixed makes the rest much easier.

The second of this set is a style I first created for a Czech/US Sudoku Championship several years ago and one that I keep bringing out every year typically for championship season. It is one of the easier styles construction-wise to get started with creative themes as it does not take a lot of digits in either grid before the linked cells really start to force the solve. But occasionally getting both grids to behave by the end can be hard. Here, my seeds were two different styles of basic step in the two grids. And after finding the linked regions, consistently ping-ponging between the two puzzles to get to the end. It is another of my favorites on this test.

Not posted this week were the great submissions from Wei-Hwa Huang. This year I gave him a sketch of the styles I wanted and he delivered in a large way. For example, I had a basic concept to play with Binary in a 6×6 grid with missing digits much like the Indian GP test had a play on this with Braille. Wei-Hwa took it farther than I did though with 0-7 and three bits being a perfect choice and his example and test puzzle were both quite fun. The Property Sudoku also had quite an elegant solve and his Diagonal had a good, but fair, challenge.

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Theme: United States

Rules: Standard Sudoku rules except that instead of the numbers 1-9 this puzzle uses the letters ADEHIMNOT. Also, clues in the grid represent typical “Seek and Spell/Kanaore” clues; specifically, it must be possible to read each of the words/phrases listed below the grid by starting at the indicated number, moving one cell in the direction indicated by the arrow, and then continuing to move one cell at a time up, down, left, or right to complete the word/phrase. No cell may be used more than once in a single path, but the same cell can appear in the paths of different words/phrases.

Answer String: For the USSQT, the answer strings were a set of rows/columns encountered late in the puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

PDF

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Theme: Logical

Rules: Standard Sudoku rules for each of the two grids. There are three shaded regions in each grid. The shaded regions must exactly match between the puzzles, but which shaded regions correspond to which must be discovered.

Answer String: For the USSQT, the answer strings were a set of rows/columns encountered late in the puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

Two more from the US Sudoku Qualifying Test in May.

The first, a Tile Sudoku, is a pattern I’ve used before but not in my recent GMPuzzles series of Tile Sudoku. Like almost every single one of these Tile Sudoku, there are “meta-constraints” forced by the geometry change that make the solve easier. First, all the 2×2 squares form a 1-9 set, which is not that hard to prove. But did you notice that each 1×3 rectangle made out of a 1×2 + 1×1 cell is part of a triplet of such rectangles that will contain the digits XY, YZ, and ZX? Because each of these 12 groups of linked 1×3 rectangles need at least one given placed into them, this 16 given puzzle is pretty close to minimal for the geometry. This puzzle’s goal was to have a clean 1-8 clock in one of the two symmetric groups, and then a choice of the remaining digits to leave a non-trivial solve even if solvers know about some of the hidden groups.

The second puzzle – Dynasty Sudoku – was a newer style for me. It’s an idea I’ve had in the back of my head to use a lot in a kind of follow-up to Mutant Sudoku. But I had not put it to paper before Adam R. Wood debuted it on the 2011 USPC. Of course his grid needed irregular regions and a 12×12 size to get a lot out of the dynasty rule. I challenged myself to make an interesting 9×9 puzzle with regular regions that still required several deductions based on not closing off the white spaces and I think I succeeded with this puzzle.

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Theme: Pattern in regions and digits

Rules: Standard Tile Sudoku rules.

Answer String: For the USSQT, the answer strings were a set of rows/columns encountered late in the puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between Sudoku number entry mode and a shading mode to mark the black squares.)

Theme: Logical

Rules: Variation of Sudoku rules. Place the digits 1 through 7 and two black cells in each row, column, and 3×3 region. Additionally, the black cells do not touch each other on the edges, and the white cells must form a single connected region.

Answer String: For the USSQT, the answer strings were a set of rows/columns encountered late in the puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

As promised, here was the original Thermo-Skyscrapers created for the USPC. I like the visual pattern and tightness of solving path much more, but it was simply too hard to use, particularly before the practice you now have from the one you saw on the USPC from yesterday’s post.

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Theme: No given numbers, and full clue cell symmetry

Rules: Standard Skyscrapers rules. Also, as in Thermo-Sudoku, digits must be strictly increasing in all thermometer shapes from round bulb to flat end.

Answer String: Enter the seven digits inside the grid for the 7th row from left to right, followed by a comma, and then the seven digits inside the grid for the 4th column from top to bottom.

Solution: PDF