by M. Sean Molley, Brian Schoner, Greg Pliska, and Tanis O’Connor
with assistance from Guy Jacobson, Kiran Kedlaya, and Sarah Bagby
Problem: Holi Town/​Pi Day Town

Solvers might recognize the circular grids in this puzzle as variants on the Seven Sages puzzles created by Patrick Berry and published in the Wall Street Journal. In a Seven Sages puzzle, each clue yields a seven-letter answer that must be filled into the spaces surrounding the corresponding numbered tile in either a clockwise or counterclockwise loop. The starting location and orientation for each answer are to be determined by the solver. A Seven Sages puzzle typically contains a quotation from a well-known “sage” around the outer ring.

Here, each of the first three puzzles contains a hidden message on one ring which can then be applied to the corresponding ring on the fourth puzzle to yield the final answer.

The first puzzle (introductory text: “One sage hid something in this mosaic, but she dropped it and the pieces went everywhere”) works like a cross between a Pathfinder and a Some Assembly Required, although many of the letters in the grid are checked more than twice. When the grid has been completely assembled, reading the letters around the inner ring gives the message TURN CENTRAL RING PI RADIANS.

The second puzzle (introductory text: “One sage found a marvelous clue for you, but some parts of this grid were too small to contain it”) is a normal Seven Sages grid except that some of the entries are trigrams instead of single letters. All of these entries are symmetrically spaced and all of them are on the middle ring. Upon completing the grid, reading just the trigrams yields FOR THE MIDDLE ONE A QUARTER TURN CLOCKWISE.

The third puzzle (introductory text: “One wise old [SAGE] left you a mes[SAGE], but he was very self-effacing about it”) is “SAGEless”—all the SAGE strings in its clues have been removed. Its outer ring reads SHIFT LETTERS ON THIS RING FORWARD FIVE AND READ DOWNWARD.

The fourth puzzle is an ordinary Seven Sages puzzle. When filled, the outer ring says TO MAKE THREE RINGS CUT CIRCLE NICELY HALVING TRAPEZOIDS.

Solvers should take the fourth grid, cut it into rings using the two “circles” that pass through the numbered trapezoids, then follow the three instructions:

  1. Rotate the innermost ring 180 degrees. (TURN CENTRAL RING PI RADIANS.)
  2. Rotate the middle ring 90 degrees clockwise. (FOR THE MIDDLE ONE A QUARTER TURN CLOCKWISE.)
  3. Shift the letters on the outermost ring forward 5 letters. (SHIFT LETTERS ON THIS RING FORWARD FIVE AND READ DOWNWARDS.) Note that only the six letters at the very top and very bottom of the main grid actually matter. Reading down the central “column” of the manipulated master grid, solvers can spell TRY ANSWER NONAGENARIANS.

Below are the three completed grids, as well as the clue answers for each puzzle.

Pathfinder/Some Assembly Required

1abandonVerb with “all hope”
2accident“That was no ______ !”
3altersWhat Darth Vader does to deals
4anodeWhere some current flows
5AntoninDvořák opening?
6BalrogDurin’s Bane, e.g.
7barterCommon transaction on Catan
8BatmanFilm superhero most recently portrayed by Ben Affleck
9beigeColor of a Federal Reserve Board “Book”
10BetamaxSony discontinued this in March 2016
11burnIt might be good when it’s sick
12CanadiansHowie Mandel and Alex Trebek
13ChaseSalmon with a big bill
14cuts in onSteals a dance partner from (3 wds.)
15decanterWine receptacle
16decimalIn math, it has a point?
17DernSurname of father and daughter with adjoining stars on the Hollywood Walk of Fame
18didgeridooInstrument that puts a Minotaur in play, in Magic: The Gathering
19DorcasBiblical seamstress
20ebbedMoved away from the shore
21enter“Speak, friend, and ______”
22examClass act?
23expelGive the same fate as Hagrid or Scamander
24iglooNorthern hemisphere?
25ignoresTakes no notice of
26ionsCharged particles
28kaleBrassica oleracea cultivar
29lancetSurgical instrument with a journal named after it
30latteStarbucks order, perhaps
31MaleDensely populated world capital originally known as “King’s Island”
32ModeloGrupo known for a namesake beer
33namasteLast word in yoga
34on tapHow one might serve #32 (2 wds.)
35Oogie_____ Boogie
36ordinalFirst or third
37PalanceBrando’s understudy in A Streetcar Named Desire
38palateA chef’s is refined
39PantoneCompany whose 2019 Color of the Year is Living Coral (“this life-affirming shade invites us to reach out and touch”)
40percussionistEvelyn Glennie is a notably deaf one
41piratesStrait of Malacca danger
42RadarPalindromic M*A*S*H character
43ramenCollege student’s go-to meal
44ReznorNIN frontman
45RideFirst American woman in space
46Rockapella“Where in the World is Carmen Sandiego?” group
47RolandWielder of Durendal
48SacramentoBee town
49seahorsesStorm, Imp, and their ilk
50sexpertSavage, for one
51speltAnother name for dinkel wheat
52StreepRecordholder for most Academy Award acting nominations
53stubbedHurt, as a hallux
54ToledoHoly city?
55ZergStarCraft race known for its “rush”


1“Estoy aquí”Shakira’s 1995 Latin Pop chart-topper (2 wds.)
2prairieBig place for a Little House?
3SpartiateOne of the Homoioi
4psi loopStructural motif first identified in the aspartic protease family (2 wds.)
5toolmakerBlack & Decker or DeWalt
6PermiakMember of a Russian-Finnish group associated with the Komi
7C.A.P. TurnerDesigner who patented the Spiral Mushroom System (2 wds.)
8precystIn some parasitic infections, developmental stage following trophozoite
9cyclonistOrganic particle effects plug-in once made by DigiEffects
10NicosiaOnly world capital with two time zones
11wisecrackSmart aleck’s remark
12ratlineLadder-like part of a ship’s rigging
13fertiliseAmend soil, as to help your rocket or courgette crop grow
14feedersThe Arkansas and Illinois, vis a vis the Mississippi
15Forrester“Finding” follower
16reactorThere’s one in NW12
17The OthersIt opens with Nicole Kidman saying “Now children, are you sitting comfortably? Then I’ll begin.” (2 wds.)
18sea starMarine celebrity? (2 wds.)
19Midas ListForbes venture capitalist ranking (2 wds.)
20lankestMost limp
21lean-earedHaving thin handles (hyph.)
22reptileCold-blooded creature
23stationedPlaced at a base
24SamoyedReindeer-herding dog
25aquaphileMichael Phelps, e.g.
26art-rapperMaker of avant-garde hip-hop, like Open Mike Eagle (hyph.)
27preinsertPut into beforehand
28unspurnedNot yet rejected by a lover
29closed setℤ in ℝ, e.g. (2 wds.)
30backwaterEpithet for a rural town, perhaps
31tablewiseAligned with the nave, rather than the altar
32forswearsMakes a Lenten promise, e.g.
33relathersSoaps up again
34ideal normKind of commutative algebra mapping, or best possible Cheers character? (2 wds.)
35worldletsSmall celestial objects or planetoids
36loneliestLike the number one, in song

Outer Ring

tsp.5 mL
rte.Mass. 9 or U.S. 20
MimMerlin’s nemesis Madam ______
caretsEditorial insertion marks
CoeRunner Sebastian
centredIn the middle, in Middlesex
sta.Kendall/MIT, e.g.
cheatCopy another’s exam
lieGolf ball’s position
keaAntipodean parrot
EPAScott Pruitt’s former dept.
tamA toorie bunnet


1hatlessSan[s a ge]ntleman’s headwear
2Fiat UnoItalian supermini launched in 1983 (2 wds.)
3last not_____ least (2 wds., uncommon)
4aetatisAt a certain year of one’[s age], from the Latin
5E.U. stateA Schengen vi[sa ge]ts you into one (abbr.)
6ReutersNew[s age]ncy headquartered on Canary Wharf
7on orderRequested but not yet received, as goods by a busines[s age]nt (2 wds.)
8RothmanHe’[s a ge]ophysics professor at MIT
9PyramisCompany founded by Alexandros Bakatselo[s age]d 27
10CypriotEli[sa Ge]orgiou, e.g.
11not longFor a short time (2 wds.)
12foist onForce (someone) to deal with (2 wds.)
13wristedMade a certain shot, in hockey
14arettedImputed, as a fault (obs.)
15fleetedMoved or passed quickly
16deliverAdminister, as a do[sage]
17free airWelcome gas station sign, for a driver with a flat (2 wds.)
18grinderDevice for preparing meat for sau[sage]
19metererWith “net,” denote[s a ge]nerator/consumer on an electric grid
20mandateDecisive vote for a party’[s age]nda
21randoriTerm for “free practice” in judo
22writtenOn paper, like the works of Le[sage]
23gatewayPoint to acces[s a ge]ographical area, perhaps
24goes dryBan[s Age]nais wines and other spirits (2 wds.)
25LoremenJames Shakeshaft and Alasdair Beckett-King podcast
26FortuneMagazine where Jame[s Age]e worked after college
27satorisStates attained by Japanese [sage]s
28die-castLike Matchbox or Corgi cars (hyph.)
29NiebuhrTheologian and [sage] who wrote the Serenity Prayer
30ChunnelPas[sage] from Britain to France
31tennistFederer or Nadal (in uncommon u[sage])
32alpisteThe seed of canary grass (var.)
33fur-cladLike a target of PETA’[s age]nts, clothing-wise (hyph.)
34rug millKaragheusian factory alluded to in Springsteen’s “My Hometown” (2 wds.)
35milkierMore like a light vi[sage]
36iterateSay or do again

Master Grid

1maillotOne piece at the beach?
3RidpathOn the Edge author Michael
4terriesTowel fabrics
5boosterSecond shot
6NairobiCapital whose name comes from the Maasai for “cool water”
7GaiaresGame featuring Zz Badnusty
8recusedStepped aside, in a way
10orarionStole from a deacon
11caravelNiña, for one
12Van VeenHead of Global Creative Strategy at Facebook (2 wds.)
14sidle inEnter as a crab might (2 wds.)
15diarchyPlace with two rulers
16percaleSheet material
17Type VIIMost common variety of WWII U-boat (2 wds.)
18rantingCarrying on
19trasherVandal, often
20heapingLike a trencherman’s plate
21in a dazeConfused (3 wds.)
22AddarioPhotojournalist Lynsey
23dragonsToothless and Mushu, e.g.
24TorontoRaptors’ home
25MangirlComic by Kagari Tamaoka
26named toAppointed as, as a government position (2 wds.)
27OneNoteOffice component
29treatedPicked up the tab
30zero airAtmospheric gases cleaned to remove almost all impurities (2 wds.)
31ten ironMost steeply angled golf club that is not a wedge (2 wds.)
32last nodFinal gesture of approval (2 wds.)
33WoodleyPrior portrayer
34sea townCoastal village (2 wds.)
35ageableLike wine or cheese that improves over time
36giggledLaughed nervously