Solution: Triangular Moves


Authors: Anthony Hsu, Yifei Luo, Max Chang

Artist: Yifei Luo

The first step is to fill in the Rows Garden grid and divide the grid into 8 regions (in the casual version, the grid is already pre-divided) corresponding to the 8 Sailor Guardians' bloom answers. The 8 Sailor Guardians can be easily identified by a Google image search.

Here are the answers to the grid clues. In the casual version, answer lengths were provided in parentheses for the row clues (as shown below), whereas in the expert version, they were not.

AScurry off (9)SKEDADDLESailor JupiterFiddle (with)TINKER
BCollide (6)IMPACTHot and humidSULTRY
Cut off (5)SEVERNarcissismVANITY
Farm sound (4)OINKNarrate a second timeRETELL
A rocky walk (6)WADDLEPossible end to a conflictTREATY
CConcealed opening (8)TRAPHOLESailor MarsExcellentSUPERB
Ridiculous (6)ABSURDFormer actor and presidentREAGAN
First satellite (7)SPUTNIKLoved deeplyADORED
DMathematician known for a category of primes (8)MERSENNERegister (2 wds.)SIGN UP
It can be savory or sweet (5)CREPESomething you might grab with coworkersDRINKS
Someone unsure whether a higher being exists (8)AGNOSTICSailor MercuryBecame smallerSHRANK
EAudio communication protocol and file format (4)MIDILeftoverUNUSED
Measure of purity (5)KARATSomeone who obeysABIDER
Free software collection or animal (3)GNUStared angrily atGLARED
Molecule involved in making proteins (3)RNAValley with steep sides common in the Pacific NorthwestCOULEE
Presidential candidate involved in recount (2 wds.) (6)AL GORESailor MoonAlaskan national parkKATMAI
FShine brightly (5)GLEAMDoomed whaling shipPEQUOD
Something to play with (3)TOYExpression for addressing more than one person (2 wds.)YOU ALL
Speech impediment (4)LISPNon-wizardMUGGLE
Top-level domain used by most schools (3)EDUTarget of beesNECTAR
More embarrassed (6)REDDERSailor NeptuneA la PicassoCUBIST
GForrest ___ (4)GUMPArmy of computersBOTNET
Sameness (8)EQUALITYRejectionDENIAL
___ cost (4)SUNKSenior executive who worked at Oracle and Google CloudKURIAN
Part of a dog breed common in memes (5)SHIBAWhite ___CASTLE
HProperty (4)LANDSailor Saturn___ FarmANIMAL
___ space (5)OUTERAgreeCONCUR
Central part of a church (4)NAVEJazz big band leaderKENTON
Inhabitant of the moon (8)LUNARIANPatch once moreREMEND
IType of acid (5)AMINOSailor UranusBestowIMPART
Building block of organisms (4)CELLCommunication devicesPHONES
Attempt (3)TRYLess lightDIMMER
Fuel-saving mode (3)ECOSomething to get rid of during fall cleaningLEAVES
Site of a World War II siege (6)TOBRUKVessel for the deadCASKET
JIt rises on a hot day (7)MERCURYSailor VenusArousing genre of fictionEROTIC
Bone in the foot (5)TALUSBook readerKINDLE
Bro or sis (3)SIBDrag one's feetDAWDLE
Annoy or irritate (someone) (6)NETTLEWears (2 wds.)PUTS ON
KOne may secure a rope (7)ENDKNOT
Unite again (6)REKNIT
Dead end (hyph.) (8)CUL-DE-SAC

The filled in grid looks like:

Each of the 8 regions is an independent triangular chess puzzle. Triangular chess is hinted at from the title of the puzzle ("Triangular Moves") and the chess-themed flavor text, which includes chess words like "check," "mate," "king," "queen," and "knights." The word "unicorns" in the flavor text helps confirm triangular chess, as the unicorn is a new piece added in triangular chess that is not present in standard chess. It also helps disambiguate triangular chess from another chess variant called tri-chess, since tri-chess does NOT have unicorn pieces.

Each region contains exactly one hexagon with a black dot and also exactly one K, always located in the hexagon with the black dot. As suggested by the flavor text, this K is the "dark king" (K is the chess notation for king) that you must "mate" (checkmate). You mate this king using the other chess pieces in the region. The other chess pieces are the letters used in standard chess notation, plus P for pawn and U for unicorn. While P and U are nonstandard, we hope using those letters seemed natural, as they are the first letters of pawn and unicorn, respectively, and the other standard chess pieces (besides the knight) are represented by their first letter.

  • K = king
  • Q = queen
  • R = rook
  • B = bishop
  • N = knight
  • P = pawn
  • U = unicorn

In the casual version of this puzzle, the letters representing the pieces are highlighted by the capitalized letters in the flavor text words "King," "Queen," "kNights," "Unicorns," "otheR," "Buddies," and "Pals."

The other realization solvers must make is that all the chess pieces in the cells adjacent to the black dots are black pieces. This is hinted at by the phrase "the dark king (and sometimes his forces)" in the flavor text. Solvers might also come to this realization after being unable to find a mate-in-1 for some regions otherwise.

Once all the chess pieces have been identified in a region, the solver must find a mate-in-1 using the white pieces (those in cells touching white dots). Each region should be thought of as an independent triangular chess board, and pieces are not allowed to move outside the boundaries of the region (nor are pieces from other regions allowed to be used).

The solutions to the 8 mate-in-1 chess puzzles are shown below. White pieces are indicated in black, black pieces indicated in red, and extracted letters indicated in yellow (except for the 'R' that is a black piece):

For each of the 8 regions, extract the letter in the cell that the mating piece moves to. Then sort the letters by the Sailor Guardians in order of proximity to the sun (closest to farthest) to get the final answer RELATIVE.

Sailor MercuryR
Sailor VenusE
Sailor MoonL
Sailor MarsA
Sailor JupiterT
Sailor SaturnI
Sailor UranusV
Sailor NeptuneE

Authors’ Notes

The puzzles in this COO round each involved 3 elements. The 3 elements we were tasked with for our puzzle were anime, grid, and triangles.

Initially, we were thinking of using the anime Kantai Collection, which involves girls in a naval school that put on weaponized outfits and embody the spirit of historical warships. We were going to combine that with a battleships logic puzzle on a triangular grid (inspired by this year's MITMH puzzle Dancing Triangles). However, we found out that another puzzle already involved a battleships logic puzzle, so we scrapped this idea.

None of this puzzle's authors is super into anime, so we did some more brainstorming focused on "grid" and "triangles," with the belief that we could tie in "anime" later, since there seems to be an anime about everything. Thinking about "grid" and "triangles" naturally led us to think about triangular grids. This reminded us of a Rows Garden puzzle grid. We wanted to combine this with some logic component, so we searched for games played on triangular grids and eventually stumbled upon triangular chess.

We needed some way to order the letters extracted from the 8 regions (this gave us a bit more flexibility in constructing the grid vs. needing to have the letters read in order left-to-right, top-to-bottom), so that's where we thought to incorporate the Sailor Guardians.

In constructing the grid, the Rows Garden app was super helpful. We also used a lot of OneLook to find valid words.

Initially, the flavor text was a bit coy about chess and referred to Pegasus, a horned horse in the Sailor Moon universe, rather than unicorns, to be more thematic with Sailor Moon. However, during initial test solves, we found playtesters going down Sailor Moon rabbit holes and not finding triangular chess. So we adjusted the flavor text to downplay the Sailor Moon references and add more explicit chess references.

In subsequent test solves, we found that playtesters realized there was chess involved but they were having trouble identifying the correct chess variant. The fairy chess piece Wikipedia article has a fairly comprehensive list of fairy chess pieces and lists many chess variants that involve unicorns. However, it was missing triangular chess, so we edited the article and added it. We also tried to add triangular chess to the glossary of chess Wikipedia page but that edit was quickly reverted due to not being a "commonly used [chess] term."

Once solvers found the triangular chess Wikipedia page, they often still had trouble understanding how pieces moved. To make the moves easier to understand, we added 6 diagrams to the triangular chess Wikipedia page, one each showing the moves for rook, bishop, queen, king, knight, and unicorn.

We hope you enjoyed solving our Rows Garden puzzle and learning a little triangular chess! If anyone implements a client for playing triangular chess on the computer, please let the authors know. We would love to play a game.