Act I, Scene 2

Divide and Conquer

119 solves / 644 incorrect guesses

Solution: IMPROPERFRACTION


Credits: Alex Ritter, Harish Vallury

In this beautifully typeset worksheet, we see that there are two questions. All subquestions of Question 1 turn out to be cryptic clues with the scores as answer lengths. Answers are in alphabetical order.

AnswerCryptic explanation
(a)CLEANERSCLEAR (wipe) around NE (noticable edges) + S (begin scrubbing) = CLEANERS (janitors)
(b)COMPOSITORCOM (first letters of creating our manuscript) + (I inside POST) (first letter of ink in letters) + OR (middle of word) = COMPOSITOR (typesetter)
(c)DEMANDINGDouble definition of difficult and ordering
(d)FERRIMAGNETICAnagram of "written on grimy briefcase" after removing the letters in "missed by its owner" = FERRIMAGNETIC (property of yttrium iron garnet)
(e)FRACTURESFRURES (anagram of "surfer") around ACT (show) = FRACTURES (does the splits)
(f)GERMINATEDAnagram of "garden time' = GERMINATED (sprouted)
(g)ICOSAHEDRONICOS (first letters of in confusion ought she) + AHEDRO (anagram of "head or") + N (tail of coin) = ICOSAHEDRON (has twenty faces)
(h)MATRIARCHIESAnagram of "charities arm" = MATRIARCHIES (ant colonies or elephant herds)
(i)PARDONABLEDON (professor) inside PARABLE (allegory) = PARDONABLE (permissible)
(j)PARTITIONPARTON (Dolly) around IT (pens "hit" without the starting h) and I (a) = PARTITION (break up)
(k)PISTACHIOAnagram of "sociopathic" without CO (unco) = PISTACHIO (nut)
(l)PREDATORSAnagram of "and sport deerskins" without KINDNESS = PREDATORS (hunters)
(m)RELOCATEDRELATED (affiliated) around OC (anagram of CO from company) = RELOCATED (moved elsewhere)
(n)SNOOKERINGAnagram of "snorkelling" around O (ball) - LL (remove half of "till") = SNOOKERING (in pool, trapping)
(o)STAGECRAFTAnagram of "great facts" = STAGECRAFT (about lights, costumes, scenery etc.)
(p)SUPERGIANTAnagram of "signature" and P (page) = SUPERGIANT (a huge star)

Next, Question 2 appears to be quick clues, and the answers are once again in alphabetical order.

  • (a) ACID
  • (b) ALAN
  • (c) A.C.T.G.
  • (d) CHAI
  • (e) CURE
  • (f) KING
  • (g) MASH
  • (h) M.ENG
  • (i) NAND
  • (j) RENT
  • (k) RIOT
  • (l) ROOM
  • (m) RUSE
  • (n) SCAN
  • (o) STAR
  • (p) TACO

The puzzle's title indicates that we should divide the answers to Question 1 (numerators) by the answers to Question 2 (denominators). When we match one numerator with one denominator, we divide by cancelling out any shared letters as if the letters were algebraic variables on either side of a vinculum. The quotient can be anagrammed into a word. Ambiguities in the anagramming can be discarded for now, since they do not influence the next step. The full list of divisions, in order of numerators:

NumeratorDenominatorQuotientPossible anagrams
CLEANERSSCANLEERLEER, REEL
COMPOSITORROOMCPSITOOPTICS, PICOTS, TOPICS
DEMANDINGNANDDEMIGMIDGE
FRACTURESCUREFRATSFARTS, RAFTS
FERRIMAGNETICMENGFRRIAETICARTIFICER
GERMINATEDRENTGMIAEDIMAGED
ICOSAHEDRONACIDOSHERONONSHORE
MATRIARCHIESMASHTRIARCIECRITERIA
PARDONABLEALANPRDOBEPROBED
PARTITIONRIOTPATININAPT, PAINT, PATIN, PITA
PISTACHIOCHAIPISTOPOSIT
PREDATORSSTARPREDOPORED, ROPED
RELOCATEDTACORELEDELDER
SNOOKERINGKINGSNOOERNOOSER, SOONER
STAGECRAFTACTGSERAFTFASTER, STRAFE
SUPERGIANTRUSEPGIANTTAPING

When in doubt, just apply the mechanism again! Let's try and divide the quotients amongst themselves.

Quotient 1 (numerator)Quotient 2 (denominator)Quotients' quotient
CPSITOPISTOC
FRRIAETICTRIARCIEF
GMIAEDDEMIGA
OSHERONSNOOERH
PRDOBEPREDOB
RELEDLEERD
SERAFTFRATSE
PGIANTPATING

The quotients' quotients are the first eight letters of the alphabet! This strongly suggests an ordering system. Perhaps we should order our first set of quotients by what their corresponding quotients' quotients are.

Quotients' quotientQuotientPossible anagrams of quotient
AGMIAEDIMAGED
ADEMIGMIDGE
BPRDOBEPROBED
BPREDOPORED, ROPED
CCPSITOOPTICS, PICOTS, TOPICS
CPISTOPOSIT
DRELEDELDER
DLEERLEER, REEL
ESERAFTFASTER, STRAFE
EFRATSFARTS, RAFTS
FFRRIAETICARTIFICER
FTRIARCIECRITERIA
GPGIANTTAPING
GPATININAPT, PAINT, PATIN, PITA
HOSHERONONSHORE
HSNOOERNOOSER, SOONER

Reading off the possible anagrams, we see that the unambiguous anagrams' first letters spell IMP??PE???ACT?ON. A few trials (and educated guesses) should reveal the final answer of IMPROPER FRACTION. The way we've been doing fractions in this puzzle is certainly improper!


Authors' notes

We feel what caused the most strife in this puzzle are the ambiguous anagrams. During test-solving, the ambiguities were picked up but the test-solvers felt they had enough unambiguous anagrams to go on to reach the final answer. This was why we didn't think too much about it. Preliminary feedback from real solvers, however, was rightly critical of this, and we should have done more to correct for it. Perhaps the easiest way around this was to clue for the desired anagrams (vaguely but enough to distinguish which anagram we wanted), and we do regret not implementing this.

That aside, most teams seemed to be able to crack this puzzle in the end, which was good to see. Hopefully the other elements of this puzzle (the repeated divisions, etc.) were more palatable for everyone.