Earlier in 2021, Thomas Snyder and Serkan Yürekli from Grandmaster Puzzles constructed a Puzzle Grand Prix round. This week we are taking a look back at those puzzles and will be adding some extra notes on the constructions here.
General Thoughts (Thomas): 2021 was originally going to be a World Puzzle + Sudoku Championship arranged by some North American authors. The pandemic threw off those plans over a year ago, and has made life continue to have a lot of challenges for me as I balance a lot of science job responsibilities including COVID-19 and autoimmune research with trying to maintain this website as a side gig. Doing “extra” things like constructing this puzzle round were going to need help. So I connected with Serkan as a co-author to assemble something different for this year as we continue to prepare for Grandmaster Puzzles organizing future World Championships / puzzle events.
My mission statement for writing any competition is always the same: “Organize a competition that serves as an example for what all other competitions should strive for.” Embedded in that big objective are many of my own viewpoints as a puzzle competitor, designer, and editor.
The competitor goals are primary of all three, as the solvers’ experiences should be most important in this kind of event. My goals there include having a really balanced and fair competition round for solvers. In my view that should include a mix of very easy to moderately hard (not very hard) puzzles. No puzzles should require heavy bifurcation or guessing. A broad set of puzzle genres should be present. There should be minimal “very new” puzzle styles, particularly ideas that would motivate a top solver to do any extensive preparation to learn the style in advance — I view this as “unfair” given the different availability of time across solvers to prepare in advance, particularly for a Grand Prix round in a packed puzzle calendar. And ideally, a fair number of solvers should be able to completely finish the round so that overall skill, not puzzle selection, determines the top rankings. This year, we met all but the last goal really well. Given the compressed time we had to write and edit the round, we were probably ~15 minutes long in content. We did have one person completely finish the round, and a second finish but with an error (congrats to Freddie Hand for his top place and Walker Anderson for second!).
The design goals are usually to show something special within the round structure that makes the connection of puzzles more special. A Grand Prix round is not just 12-20 randomly collected puzzles. It should have something that brings it together. We’ve tried different ideas before, but no idea should be so experimental that it sacrifices the competitor goals above. The idea I had this year was to continue our 5-6 genre structure but identify two puzzle styles within each genre that could be recombined to make a third “hybrid” puzzle. Moreso than just making a hybrid, I wanted a lot of the grid elements from the original puzzles to be reused in the hybrid puzzle. That way, a solver going through the three puzzles together would sense a stronger experience than just three separate grids with no joint story. As you’ll see as we get through this week, there were some fun stories across the grids.
But we probably fell short on the last set of “editor” goals in that the arrangement of the puzzles throughout the competition separated the stories from each other. So this week we’re breaking the content out from the original competition booklet form (which no longer seems to be available online) and giving you the six puzzle vignettes across the week. They represent the five common genres we use on the site (all except for “Sudoku” which has its own Grand Prix structure), adding in a sixth of “Word/Observational” puzzles to get additional styles that appear at World Puzzle Championship Events.
We’ll be adding new stories here with each set of web posts:
Loop puzzle set (Thomas): This “Triple Threat” set combines the same visual clues across the related styles Yajilin, Castle Wall, and a hybrid combining these. This “Triple Threat” was the last set of puzzles I wrote but ended up being the easiest across all three so starts off this week. I always worried this group might be the most visually elegant but least logically elegant of the set. That is because I wanted a true triple where ALL the numbers and arrows were preserved across the Castle Wall and Yajilin styles (which share a visual style) and only having box coloring lead to three fairly different solves. Castle Wall colors would be preserved in the hybrid version as well, with ~50% of cell colors coming from each component grid. That’s A LOT of constraints. With three dependent grids, any one that didn’t work would require tweaks that affected the other two and potentially compromise the logical flow.
I started the construction with a fairly open grid and two seed clue locations. One key seed was the 3 down column 1 clue, paired with a black cell in R8C2 to have three different openings for Yajilin, Castle Wall, and the hybrid. The hybrid’s need to fill in all the cells but also keep black clues outside of the loop made the three down clue have three different looks across each of the puzzles. Another seed was the 1 right in R9C7 and 3 down in R3C9 which, connected with unspecified clue cells in the two places you end up seeing them, put in both Yajilin and Castle Wall tension. You can’t easily shade three black squares in that 9th column. You also can’t get 3 vertical line paths for Castle Wall with the intersecting 1 right clue in row 9. The hybrid shifts to use one Yajilin and one Castle Wall coloring to differ that corner again.
Everything else came from forward solving from those two seeds, with eventual values and colors for each of the clues coming from whichever of the three grids was least constrained and seeing if something helped at least two of them. This sounds much easier than it was, and I had to undo about two or three ideas all the way back to the initial seeds before this worked. Overall I probably took 6-7 hours to make these three puzzles, far more than usual. But I hope you enjoy the different solves; truly this is a loop genre served three ways.
Shading puzzle set (Serkan): These two styles can’t use all of the same clues as they would repeat the same solutions. But taking some of the clues from each classic style could make an interesting hybrid. So I needed to choose clues in LITS (Tapa) without changing the clues I used in the Tapa. In the hybrid puzzle I also needed to change some of the regions in LITS; otherwise I would have had a hybrid puzzle that is solvable by very similar logic. So, I knew that I had to change regions to move more freely, using small changes like bringing together neighboring regions. This would allow the final puzzle to look as similar to LITS as possible but solve quite differently.
I wanted to have a host country icon here, as I have done many times in USPC puzzles before. It was not difficult to write a US in the center with LITS regions. I made them just one unit wide, so the letters U and S didn’t cause too much trouble in setting a single tetromino placement compared to the challenge you can get as a designer from much larger regions. My other goal was to preserve these areas in the final puzzle no matter what, to make them visible in the same place. Even though I chose to split the letters U and S in the last puzzle, the US continues to be clear. In the grid, the last puzzle was easier than I expected, as there are too many constraints.
This group was the one I created in a shorter time than the other two groups. But of course, although it was short, I still put a lot of effort into it. I spent about 22-27 hours for three groups of 9 puzzles in total.
Region Division puzzle set (Serkan): Bringing all three puzzles together from this genre was difficult for this kind of build. But here, both Pentominous, Spiral Galaxies and the combination (marking symmetric pentominoes like in Spiral Galaxies) fit into the same category of Region Division.
I wanted the set to be somewhat difficult, but due to Pentominous the grid sizes had to be multiples of 5 and I had to be aware of the size. In recent years we have started to give black squares for puzzles of this type, although it wasn’t my first choice to give them away if the black squares don’t serve a theme. Still I managed to keep their placements in the last puzzle.
Pentominous was the main resource; I could get different placements in the final puzzle by removing some letters from the main source but kept the symmetry of the letters used in the combination puzzle. I also knew that when I was making Spiral Galaxies, I had to build large structures. In the final puzzle I’ll keep the dots, at least by means of the letters, so those large areas could have been divided differently.
I made a trio that serves exactly those goals. Most of the letters and most of the circles remained in the final puzzle; Although it looks very similar to the first two puzzles, I got a hybrid puzzle with a different solution path.
Object Placement puzzle set (Thomas): This was the first trio of the competition to be written and was the example used when agreeing the theme was a good one for the full round. While the visual combination of Star Battle regions and outside Battleships clues would make the shared elements in the three puzzles quite clear, the distinct nature of the constraints — particularly changing 2 non-touching stars to having 2 ship segments in a region — would make the puzzles naturally solve in different ways.
Battleships is usually the first puzzle in the United States Puzzle Championship. So given the flexibility of other ship/sea clues in the regular Battleships which would not go to the Star Battleships hybrid, I had a second goal to emphasize the US round again here and make the Battleships be the easiest puzzle to go first. (It did end up being the easiest puzzle but was set-up to go elsewhere in the round when finally posted.)
My construction here started from connecting a few seed ideas across grids. When writing a Star Battle, one of the themes I sometimes explore is coming up with a simple repeated shape that can sit together a lot. The crescent pattern (two sitting under a full circle, and two others interlocking with a turn) were five quick regions I put into the grid, thinking I could force some row-by-row tension in the propagation of stars. I then also put in the 2345 series of Battleships clues, knowing the 45-clued rows would also be a big point of tension. And finally, in the combination puzzle I wanted to have just five regions spanning those 45-clued rows with some other clue or interaction making a maximum of nine ships across those five regions be the break-in to that puzzle. With all those seeds working together in rows 6 and 7, solvers hopefully experienced some déjà vu of similar starting points even if the puzzles flowed differently from there.
I then completed the construction in the order Star Battle –> Star Battleships –> Battleships to work through the constraints in order. Keeping the top of the Star Battle spanned by one big region started a good partial star cascade in rows 2-4, getting the crescent shapes working together including places where a star in columns 2/3 or 8/9 force a star in only one but not both of (columns 1/4 or 7/10) in rows underneath. It also set up a second tension of either/or placements that would work in tandem to place two stars in the same columns (either 7 or 10) at the top of the right side of the grid that was probably a necessary deduction to get to the one answer.
With the regions from the Star Battle then set, I turned to the hybrid puzzle and added in a few more ship clues (particularly all the columns with symmetry of 30 / 03) to get a nice solving path for that grid. It began from the intended 45 seed but then worked into some 2-unit and 1-unit ship counts as adjacent regions were filled with ships. Completing the set for the main Battleships, I tried two orientations of U and S clues with a lot set by the 45 rows right away. I had some options to get ~10 solutions down to 1, and decided I liked the look of two symmetric subs versus other options with more seas or more row clue numbers added. Overall, I was happy to have three distinct puzzles but with some common seed locations and fully repeated visual elements that solvers might notice between the different puzzles.
Number Placement puzzle set (Thomas): “Half and Half” was the initial idea for the theme of this combination, with a diagonal split of two Latin Square puzzles coming back together for the synthesis. The diagonal theme concept led to the bent triomino pattern for the TomTom early on, with six of the twelve clued cages being reused. I also intended for a common Skyscrapers theme element (an increasing digit series) to be used on each of the two shared sides of the Skyscrapers half which can set up some interesting ladders and hidden pairs in some cases.
The construction started with the TomTom, where I set all the clues that end in 0 first. Some of these are obvious products, and my main focus was adding a lot of 20s where there are 3 options (145,225,677). I wanted the two adjacent 20s in the shared TomTom half to be reused in the combination puzzle, so when I got to setting up the skyscraper clues I put in a 3456 series that would force a 7 building outside the two 20s and eliminate the 677 option. This puts 1245 in the first four cells in row 1 (and 2 and 5 in the triomino cells in row 2). It also helps specify the last triomino in the top which became an 11 in the final puzzle, given just the 367 digits that remain in that first row. With a joining clue concept across the grids, I still needed to finish the TomTom construction but now started to build the SkyTomTom pair at the same time as the identities of the clues on the left side would need to be used by both grids. The large 16 and 15 clues are good as TomTom clues (possible sums and products) but also could capture the large 7’s that looked to be moving to the left side in the SkyTomTom grid.
While I got the TomTom and SkyTomTom working fine, I had only half a Skyscrapers puzzle and some uncertainty I could get an interesting puzzle out of it although the two consecutive digits series, from past construction experience, should help a lot. The first clues to go in were the 6 and 2 on row 1 and 7 (expecting I would add two clues that were 2 or larger into columns 1 and 7 to finish the puzzle). This locked in all the 7s and did set up a fun set of hidden pairs in the middle columns, but there were still six valid solutions. I liked the symmetric clue of a 5 near the 6 and this did get to a unique answer with another unrepeated clue for top/left of 3 in the seventh column.
This was a set I was particularly happy with, both that the visual theme elements worked cleanly, the solves had some shared elements like thinking about 20 cages, but with very different ways the grids played out that felt like all could stand on their own as solid competition puzzles.
Word Placement / Observation puzzle set (Serkan): This was the most difficult trio to design. The first challenge was deciding which three genres to use. Before deciding on the idea of “Meandering”, I also considered different types of puzzles but the number of rules was not enough. I had to choose a genre which was not only a word puzzle but also should give an option for words to be placed differently. So the Meandering idea was the best fit because of the word placement and letter placement rules. This could combine with the “word search” idea to make a complete set.
I only kept a few of the letters which I used in the Word Search for other puzzles; the main goal was to move the central 3×3 region to the other puzzles and keep it the same in all three. I was going to maintain most of the letters in the transition from Meandering to the final puzzle which I did; I moved all 7 letters to the last puzzle in the same way, and only one pair of grid boundaries had to change.
Another challenge was the words I would use. If words change constantly from puzzle to puzzle, which would be necessary, the transition between the three puzzles would not look very clean. Moreover, the solver would have difficulty in the face of the ever-changing word list. Therefore, there should be a single list and the words in that list should have been used in different combinations from puzzle to puzzle. Such a word list should not consist of random words. In word puzzles, the theme is not just in the puzzle grid but also in the chosen words. The list should have been about the US, as it was the US leg of the GP. So I thought the best word list would be American writers. It was very difficult to finalize the list in this way, because some words were not suitable for genres. After long hours, which I think I’m talking about between 15-18 hours, both the list has been finalized and the puzzles have taken their final form as you can see.
Additional note from Thomas: I agree that this construction idea was really novel. The discovery of Word Search placements during the big Meandering Word Search was a delight and that hybrid was fun for the challenge. This was the one puzzle set where there were many editorial choices and possibly other options could have improved it for competition like: (1) adding more gray squares to Meandering Words which had a very narrow solving path, or (2) making a more solver-friendly form of the word list alongside the themed version, since many solvers will sort by length during their solve. The diversity of US authors (some who have probably never been listed together) was another curiousity but added to the character of the puzzle set.
We welcome your own comments on the round, questions on the designs, and other feedback about Puzzle Grand Prix rounds.