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

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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

This puzzle was inspired by a comment I read somewhere of someone stumbling on a Thermo-Sudoku by solving it for awhile as an Arrow (or vice-versa, I can’t remember exactly). The goal was simple: can I make one puzzle that solves both ways depending on the type of shape placed into the grid. The theme here speaks mostly for itself.

But if you want an extra challenge I’d recommend solving from these images (Arrow / Thermo) or PDFs (Arrow / Thermo) which contain the original draft of the finished puzzle. The arrow is probably a much better challenge as a result, but the Thermo is at the very high end of the difficulty scale and better for a slow solve than a competition solve. Fortunately there were a good set of symmetric positions that still matched with digits so I could add clues to both puzzles without spoiling the theme. Of course, almost all the remaining digits differ but I guess that is the point.

Some people have asked about the construction steps to get two working puzzles of very different types. I normally design both of these styles by hand starting from an image of the shapes and then slowly adding digits. Here I simply did this at the same time for two different styles. The intention of having the centers work quite differently in the two types made the first four givens in the center the start. The 1’s in the corners were also great clue digits for both Arrow and Thermo types for different reasons. As I got some other good logical placements worked out, I did use some software tools to confirm each puzzle still had possible solutions before going too far down a dead-end. Gradually a duplicated puzzle came into form.

Enjoy what were probably my favorite puzzles from the USSQT.

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Theme: Deja vu

Rules: Standard Arrow 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

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Theme: Deja vu

Rules: Standard Thermo-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

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

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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

Two more from the US Sudoku Qualifying Test in May — both geometric departures from regular sudoku.

As I consider the 2012 Irregular on the USSQT one of my best puzzles from that year, it was obviously going to be a challenge to do as well this time around. I felt the puzzle below was an adequate follow-up but certainly not as good as last year’s. The solve is meant to take advantage of the slightly irregular spacing of 1-6 in the patterned middle with the extra 7’s and 8’s giving a single solution. Note there are no 9s anywhere in the grid. Some Law of Leftovers steps will likely be encountered before the finish.

For the isodoku, just before the US Qualifier test, one of our readers here suggested I make a tutorial on some of the forced rules that come with these 3d shapes (this was after an isometric TomTom that strongly required solvers to know only 2 of each digit could appear on each face). I obviously couldn’t post such a tutorial just before the USSQT, but the properties of the 3D shapes was strongly in mind here. Often — like in the standard 2×4 rectangle form of an isodoku, or the 2012 USSQT Isodoku — there is a strong 2×2 square requirement that can split the digits into two distinct sets throughout the puzzle (see this colored solution of the 2012 for example). This year I wanted to choose a geometry that almost seems like it needs that 2×2 requirement in places, but here only three digits are highly constrained and the attempt to split the shape into patterns falls apart. Can you spot the three constrained digits and sort out where they must always go in this kind of geometry? Six particular cells are key.

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Theme: Pattern in regions and digits

Rules: Standard Sudoku rules. The regions are not 3×3 boxes but are instead irregular shapes indicated by the bold lines.

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

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Theme: Stacked boxes

Rules: Standard Isodoku rules, using numbers 1-8.

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 — both are styles I’ve constructed a lot of in the past and will likely continue to construct a lot of in the future as they are both pretty simple variations that add more properties of the numbers into the logic of sudoku and enrich the solving experience.

I went for a lot of less common symmetry types with this test (diagonal or mirror symmetries instead of 180 degree rotational) and both of these themes showcase one of those less common types. With Tight Fit, the diagonal symmetry works well with the added slashes forming their own diagonals parallel to the mirror plane. The solve was meant to fairly easy, but the sparsity of starting digits here actually leads to a rather large cycle to place two of the highest digits remaining towards the end of the puzzle. This trait pulled it towards the top of my pile of Tight Fit to include here.

For the Consecutive Sudoku, I’ve been doing a fair bit of half consecutive/half non-consecutive exploration recently (such as this earlier GMPuzzles one). And I’ve played with 2×2 box shapes with consecutive bars before too, such as here. Well, it turns out that there are no puzzles possible that have just the 2×2 box shapes in opposite corners as in the second linked puzzle without additional bars elsewhere. But there are a whopping 4 possible solutions with the repeated top boxes and no other bars as here (and 2 of those 4 are trivial copies from a 1-9 to 9-1 swap). It was from that small set of potential solutions that I crafted this puzzle. Using a given presentation that evokes the same kind of bars as up top seemed best and gave the solving properties I wanted. But if you’d like an extra hard challenge different from this one, put a single 1 in the lower-left corner and try to solve from there. As I’ve discussed before, the non-consecutive constraint is really powerful and constraining in ways you wouldn’t expect but it always needs some hands-on work to cultivate a fun and approachable puzzle.

Both of these puzzle are probably on the easier end for this test, but both are good representations of the new logic that arises from the variation. As “extras” from the first Grandmaster Puzzles construction cycle, it seems fitting to get them both up here now.

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Theme: Diagonal Series

Rules: Standard Tight Fit Sudoku rules. Range is 1-9.

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

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Theme: Boxes of Two Sorts

Rules: Standard Consecutive 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

The Sudoku Grand Prix (GP) has certainly now shown a variety of test styles after the creative but unorthodox Turkish test this past weekend. I’m still not sure exactly what the GP is trying to be, and I have no idea what the “playoff” in Beijing will look like (does anyone know anything about the rules or puzzle designers?), but the list of 10 competitors to qualify is getting much clearer now. Quite incredible to have a different winner for each event so far.

Our test, like some others in the GP such as the UK test, had a pretty clear goal to have a lot of elegantly constructed sudoku in pretty simple styles to test basic sudoku skills. All our puzzles had fair, logical solution paths, and we expected many solvers would finish. And as I still think of this as a US Sudoku Qualifier first, and a GP contest piece second, I was glad we got two of the qualifying Americans to submit all of the answers even if one had a mistake. While this is now quite belated, congrats to Jason Zuffranieri for his US victory and to Bastien Vial-Jaime for the overall victory.

Here is the second pair of classic sudoku that appeared on that contest.

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Themes: Both geometric and logical

Rules: Standard 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.

Design Notes (highlight to view): The third classic sudoku (and first here) was built around an even versus odd theme and recognizing this unusual partitioning of the digits will be key to making fast progress. A bunch of singles (either naked or hidden) can be found based on parity around the middle sections which finally breaks through to the final solution. The fourth classic sudoku (and second here) was constructed to have an early and pretty clear single sticking point aspect to it. The geometry suggests something should be present in the almost full rows or columns. If solvers focus on those most constrained positions in the first column, they will find a naked pair [89] that gets the whole solve going. While none of these classic puzzles required extremely difficult techniques, keeping the solving paths somewhat tight at the very start makes them good competition challenges in my mind.

Solutions: PDF and PDF

While scheduling the month of June for the site, and considering the potential for some likely downtime or errors while changing web hosts, I budgeted two weeks for recent US championship puzzle discussion. For this week, I’ve planned to cover the US Sudoku Qualifying Test (also the sixth leg of the Sudoku Grand Prix). If you are desperate for new puzzles, those will arrive next Monday at their usual time. But there may be some new challenges revealed throughout this week during the discussion of these creative sudoku.

I figured I’d give a general overview of our design process at the start. As with past years, we (Nick Baxter, Wei-Hwa Huang, and myself) had planned a two-part championship with Classics and near classic variations for the first part, and mostly new or less common styles for the second part. Some of this has been to gauge relative solving capabilities on the challenges that might appear at a WSC, and some of this has been for our own sanity checking of potential competitors. There are more web-accessible sudoku solving tools that can handle “part 1” puzzles and some unbelievable times have been posted there in the past. But less familiar or original styles in “part 2” will challenge anyone solving with certain types of assistance. After the 2009 experiences in Philadelphia at our last live national championship, we know to be extra cautious.

While having two parts was the original plan, the requirements of the Grand Prix changed our design mid-stream and a single big round was used instead. So solvers got 2.5 straight hours of solving to test their mettle. But you can see that the ordering of the puzzles still naturally splits the first ten from the last ten and perhaps many solvers found themselves focusing on just the first part instead of the other.

We like having a mix of puzzles but also a fair number of classic sudoku since a sudoku championship should certainly test the fundamentals. I wrote all 4 of our classic puzzles, each somewhat noteworthy in its own way. Their numbering was maintained in my “construction order”, as testing revealed their mean solve times were within a minute of each other and they would all receive the same point values on the test. I believe only solvers with a very broad skill set would have a uniform performance on the entire set. But just as different test-solvers reported being tripped up by different puzzles, competitors reported the same thing with #2 and #4 seeming to be outliers. I wonder what your experiences were?

I’m posting the first two classic puzzles below, with design spoilers concealed after each puzzle. The next two classics will follow tomorrow.

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Themes: Both geometric and logical

Rules: Standard 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.

Design Notes (highlight to view): The first puzzle was designed around a low/middle/high separation and has large squares made out of 1-3 and 7-9 only that provide some symmetry along the solve. For example, consider the 1 in the upper-right corner and the 9 in the lower-left corner which come from looking horizontally, followed by either 79 or 12 pairs to finish those border columns from looking vertically each allowing the last two numbers in the corner regions to be identified. This is probably the easiest of the four classic puzzles but not by much. The second puzzle was designed to require good use of pointing pairs, particularly in the upper-left boxes, involving the “8” and “9” that are lone digits. A relay of these pointing pairs through two boxes should place the first 8s and 9s that cascade to give several other digits.

Solutions: PDF and 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

The hardest puzzle I wrote for the USPC was originally intended to be presented as a subtle “surprise”. The rules would have covered what thermometer shapes do (strictly increase from bulb to flat end), but would not have been explicit that those shapes could reach outside the grid. So finding a grid with no external numbers but with many external shapes would have been a manageable but perhaps unexpected surprise. But it was decided to just be explicit here, and with some other authors in the last few months having used the same external clue ideas with skyscrapers (including myself here with an Even/Odd Skyscrapers after I knew the fate of this puzzle) it’s not clear if this would have been unexpected anyway.

I thought this was an interesting extension of some inequality skyscraper concepts I’ve seen elsewhere. My first attempt at this puzzle type was judged very elegant and far too hard. My second attempt kept one of these two traits and made it onto the test. Like the TomTom, this variation seemed to get pretty good reviews, but I do know some solvers who fell into the trap of thinking an outside number blocked that number from appearing inside the grid.

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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: For the USPC, the answer string was the internal cells in the 4th row and 7th row. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

While I still want to find a good name for this variation of TomTom (Tight Fit TomTom matches the genesis story well but is probably not the best name for longevity), it was a style idea that strongly encouraged me to write for the USPC this year as it seemed a great place to debut it.

The idea actually came from Craig Kasper during a discussion of puzzle styles and possible variations. Craig didn’t think he could do it justice, but he offered it to me and I knew instantly it was a great concept to save for the future — with the USPC as the obvious first destination if it could work. I wrote two Tom/Tom puzzles (also probably not the best name — maybe in the comments people can recommend others?). The first was an easy one (10 pointer?) that became the example. The second was a tougher puzzle that has been called undervalued for 20 points by most people commenting on it. Perhaps the break-ins were not as easy to find?

The biggest struggle with the style was how to format it well; you’ll find that both of these puzzles use slashes in cells that would not normally contain the clue digit to leave more space in the fractional cells for writing numbers. Palmer’s pre-USPC example uses shaded cells and this might be a more productive route going forward. I have plans to make a bunch of TomTom variety books/puzzle packs focused on different math concepts and will probably make one around this variation when I get some larger tasks off my plate. Removing some of the extra trickiness of these samples and having simpler fractional values and even fractional clue targets should make this a good extension of TomTom puzzles for education purposes. I can even turn single cell cages into non-trivial entries!

I hope you enjoyed this variation as much as I enjoyed making it work.

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PDF

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

Theme: Cage geometries, and the logic of the solve and new fraction rules primarily

Rules: Variation of standard TomTom rules. The indicated ranges are larger than N x N (1-6 and 1-8 respectively), and 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: For the USPC, the answer string was the 5th row and 5th column of the larger puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution 1: PDF
Solution 2: PDF