Evil Relays

Answer: RELAY GOOD TIME

Each special instruction can be applied to one of the answers to a puzzle in this hunt to yield a new word in response to the problem's prompt. Additionally, each problem has a clear numerical quantity under consideration which can be used to index into the new words:

ProblemRestoredInput WordNew WordNumberLetter
1. PECIAL CTIONS: In this roblem, all but the last six etters of each word (other than those earing in math) have been emoved.
Rlotte is flying her rplane hrough higher nsions, where the n-sional cube has 80 edges. What must she avoid?
1. SPECIAL INSTRUCTIONS: In this problem, all but the last six letters of each word (other than those appearing in math) have been removed. McCharlotte is flying her airplane through higher dimensions, where the n-dimensional cube has 80 edges. What must she avoid?HAPHAZARDHAZARD5R
2. RSPECIAL RINSTRUCTIONS: Rin rthis rproblem, rthe rletter Rr rhas rbeen rprepended rto rall rwords (rother rthan rthose rappearing rin rmath).
Rsuppose x^x^x^x... = 2. Rnow rsquare x rtwice. Rwhat rshould ryou rorder rfrom Rpad Rthai Rtoo?
2. SPECIAL INSTRUCTIONS: In this problem, the letter R has been prepended to all words (other than those appearing in math). Suppose x^x^x^x... = 2. Now square x twice. What should you order from Pad Thai Too?ICERICE4E
3. PECIAL NSTRUCTIONS: N his roblem, he irst etter f ach ord as een emoved (ther han hose ppearing n ath).
CCharlotte nd CYuval it own o lay ame f Ock, Aper, Cissors, ut o ake he ame ore nteresting, he ntroduce wo ew ptions: "Andy" nd "Hocolate Ab". Hocolate Ab ats Andy; he ugar n Andy auses Ock nd Cissors o rode; nd Andy ips ts ay ut f ts Aper rapper. Hocolate Ab s quished y Ock, ut y Cissors, nd oisoned y he hemicals n Aper. layer cores 1 oint or in, 0 oints or oss, nd 1/2 oint or raw. CCharlotte ssigns ome robability o ach f Ock, Aper, Cissors, Andy, nd Hocolate Ab, nd andomly hooses mong he bjects ach ound ccording o er hosen robabilities. Ince he s ery ocky, he ells CYuval n dvance hat er robabilities re. Et x e he eciprocal f he roportion f he ime CCharlotte hould hoose Hocolate Ab. Ow ould ou escribe CCharlotte's roficiency?
3. SPECIAL INSTRUCTIONS: In this problem, the first letter of each word has been removed (other than those appearing in math). McCharlotte and McYuval sit down to play a game of Rock, Paper, Scissors, but to make the game more interesting, the introduce two new options: "Candy" and "Chocolate Lab". Chocolate Lab eats Candy; the sugar in Candy causes Rock and Scissors to erode; and Candy rips its way out of its Paper wrapper. Chocolate Lab is squished by Rock, cut by Scissors, and poisoned by the chemicals in Paper. A player scores 1 point for a win, 0 points for a loss, and 1/2 point for a draw. McCharlotte assigns some probability to each of Rock, Paper, Scissors, Candy, and Chocolate Lab, and randomly chooses among the objects each round according to her chosen probabilities. Since she is very cocky, she tells McYuval in advance what her probabilities are. Let x be the reciprocal of the proportion of the time McCharlotte should choose Chocolate Lab. How would you describe McCharlotte's proficiency?TABLEABLE3L
4. SPECIZL INSTRUCTIOMS: Hn thhs probldm, tge penultimase lettdr nf eabh woqd (othdr thzn thore appearimg hn mash) hzs bedn shiftdd babk ay ome.
Imagime thzt ynu haue writtdn dovn a veqy larfe numbdr nn a scrzp nf papdr. Scramblimg tge digiss nf thhs numbdr, ynu obtahn a secomd numbdr. Subtractimg tge secomd numbdr frnm tge firrt ome, ynu obtahn ydt anothdr numbdr. Finalky, ynu crors ott ome nf tge digiss nf thhs thiqd numbdr, amd aqe leet wish 224798432. Considdr tge dight thzt ynu crossdd ott, thdn crumpke tp tge piebe nf papdr. Whzt haue ynu creatdd hn tge papdr?
4. SPECIAL INSTRUCTIONS: In this problem, the penultimate letter of each word (other than those appearing in math) has been shifted back by one. Imagine that you have written down a very large number on a scrap of paper. Scrambling the digits of this number, you obtain a second number. Subtracting the second number from the first one, you obtain yet another number. Finally, you cross out one of the digits of this third number, and are left with 224798432. Consider the digit that you crossed out, then crumple up the piece of paper. What have you created in the paper?CREATECREASE4A
5. SPAL INNS: In this prem, all but the fist two and last two lers of each word (oter than thse apng in math) have been reed.
Of the 72 cars who are in the gaes loge, 38 of them are plng a game of "Hide and Go Seek in the Chte Lab. At the strt of each mite, the weed-weed caer (thre are no ties in wier) who is stll plng has a 1/3 chce of qung the game, but the brst caer who is not yet plng has a 2/3 chce of sung to peer prre and jong the game. An ober noes that, half an hour into plng the game, the exed nuer of plrs wold be a whle nuer of dons. What is the obr's name?
5. SPECIAL INSTRUCTIONS: In this problem, all but the first two and last two letters of each word (other than those appearing in math) have been removed. Of the 72 campers who are in the games lounge, 38 of them are playing a game of "Hide and Go Seek in the Chocolate Lab. At the start of each minute, the weakest-willed camper (there are no ties in willpower) who is still playing has a 1/3 chance of quitting the game, but the bravest camper who is not yet playing has a 2/3 chance of succumbing to peer pressure and joining the game. An observer notices that, half an hour into playing the game, the expected number of players would be a whole number of dozens. What is the observer's name?GALLERYGARY4Y
6. PECILA NSTRUCTIOSN: N hsi roblme, eh irts ettre f ahc odr (thre hna hoes ppearign n aht) sa ene emovde, hne eh ats ow ettesr aev ene wappde.
N eh ollowign iguer, evne tu f eh ixtene quarse aev ene aintde n ronw, de, raneg, r ellwo:
BROY
R???
O???
Y???

Onsidre eh umbre f ifferetn asy uo na aitn ahc f eh emainign quarse o hta ahc olro ppeasr xactyl nec n ahc wo dn n ahc olunm. Hta houdl uo nsuer eh olumsn o?
6. SPECIAL INSTRUCTIONS: In this problem, the first letter of each word (other than those appearing in math) has been removed, then the last two letters have been swapped. In the following figure, seven out of the sixteen squares have been painted in brown, red, orange, or yellow:
BROY
R???
O???
Y???

Consider the number of different ways you can paint each of the remaining squares so that each color appears exactly once in each row and in each column. What should you ensure the columns do?
KALINGALIGN4G
7. PVCIA NVTRUCTION: In this rvble, the ivs and last evte of each four evte or ovge word (tve than hvs pvearin in math) have been evove, and the evainin evon evte evome V.
Let x avisf (1 + (1 + (1+x)/(1-3x))/(1-3(1+x)/(1-3x)))/(1 - 3(1 + (1+x)/(1-3x))/(1-3(1+x)/(1-3x))) = 1. How ivh you evcrib the top of that rvctio?
7. SPECIAL INSTRUCTIONS: In this problem, the first and last letter of each four letter or longer word (other than those appearing in math) have been removed, and the remaining second letter becomes V. Let x satisfy (1 + (1 + (1+x)/(1-3x))/(1-3(1+x)/(1-3x)))/(1 - 3(1 + (1+x)/(1-3x))/(1-3(1+x)/(1-3x))) = 1. How might you describe the top of that fraction?ROGERSOVER1O
8. ACEPECIAL INACETRUCTIONACE: In thiace problem, all inacetanceace of the letter Ace (other than thoacee appearing in math) have been replaced by the word Ace.
A aceet of natural numberace iace called "evil" if it containace itace own cardinality. (For inacetance, {3, 4, 8, 9} iace evil becauacee it haace 4 elementace and 4 iace one of thoacee elementace). An evil aceet iace called "minimally evil" if it iace evil and no proper aceubaceet of it iace evil. (For inacetance, {3, 4, 8, 9} iace not minimally evil, becauacee {3, 4, 8} iace alaceo evil). Conaceider the number of minimally evil aceetace can be made with the numberace 1, 2, 3, 4, 5. What can you uacee to remove the ink you acepilled while working on thiace problem?
8. SPECIAL INSTRUCTIONS: In this problem, all instances of the letter S (other than those appearing in math) have been replaced by the word ACE. A set of natural numbers is called "evil" if it contains its own cardinality. (For instance, {3, 4, 8, 9} is evil because it has 4 elements and 4 is one of those elements). An evil set is called "minimally evil" if it is evil and no proper subset of it is evil. (For instance, {3, 4, 8, 9} is not minimally evil, because {3, 4, 8} is also evil). Consider the number of minimally evil sets can be made with the numbers 1, 2, 3, 4, 5. What can you use to remove the ink you spilled while working on this problem?STONEACETONE5O
9. SECIA ISTRUCTION: In this poble, the scon and last ltte of each four ltte or lnge word (ohe than tos apearin in math) have been rmove.
A scre aen wtche popl go in and out of a sor. When the sor oen, only 1 prso, the one, is isid. Ate an hour, 3 popl have etere and 2 have dparte. Ate aothe hour, 7 more have etere and 4 have dparte. Ate one more hour, 1 more prso has dparte, but no one else has etere. At this pin, the aen rcord the nmbe of popl who are isid, then goes home. What is the aent' name?
9. SPECIAL INSTRUCTIONS: In this problem, the second and last letter of each four letter or longer word (other than those appearing in math) have been removed. A secret agent watches people go in and out of a store. When the store opens, only 1 person, the owner, is inside. After an hour, 3 people have entered and 2 have departed. After another hour, 7 more have entered and 4 have departed. After one more hour, 1 more person has departed, but no one else has entered. At this point, the agent records the number of people who are inside, then goes home. What is the agent's name?BLONDEBOND4D
10. FSPECI FINSTRUCTIO: In this fprobl, the last two flette of each four flett or flong word (foth than ftho fappeari in math) have been fremov, and F has been fprepend.
FmcCharlot has 8 fminio to do her fbiddi, and they will work in fpai in fspreadshee. She fwan to fassi a fspreadshe tab to each of the 8 fchoo 2 = 28 fpossib fpai of fminio. She does not want to be fwastef, so she may fassi one tab to more than one pair. Fhowev, she fwan to fensu that fdisjoi fpai of fminio get fdistin fpag. For fexamp, the pair {Mia, Sim} will get a fdiffere page from the pair {Nic, Viv}, fthou {Mia, Sim} may get the same page as {Mia, Ben}. Fsuppo FmcCharlot uses the ffewe fnumb of fpag fpossib. What is her fpreferr way to ftrav?
10. SPECIAL INSTRUCTIONS: In this problem, the last two letters of each four letter or longer word (other than those appearing in math) have been removed, and F has been prepended. McCharlotte has 8 minions to do her bidding, and they will work in pairs in spreadsheets. She wants to assign a spreadsheet tab to each of the 8 choose 2 = 28 possible pairs of minions. She does not want to be wasteful, so she may assign one tab to more than one pair. However, she wants to ensure that disjoint pairs of minions get distinct pages. For example, the pair {Mia, Sim} will get a different page from the pair {Nic, Viv}, though {Mia, Sim} may get the same page as {Mia, Ben}. Suppose McCharlotte uses the fewest number of pages possible. What is her preferred way to travel?LIGHTERFLIGHT6T
11. SPEIAL INSONS: In this prolem, all but the first three and last three leters of each word (other than those apping in math) have been remved.
Conder the leaing coeent of a degree two polial p(x) with intger coents, where p(0) = -7 and sin(2π/7) + sin(4π/7) + sin(8π/7) is a root of p(x). Assing you have no troble with it, how would you desibe your ease of soling this prolem?
11. SPECIAL INSTRUCTIONS: In this problem, all but the first three and last three letters of each word (other than those appearing in math) have been removed. Consider the leading coefficient of a degree two polynomial p(x) with integer coefficients, where p(0) = -7 and sin(2π/7) + sin(4π/7) + sin(8π/7) is a root of p(x). Assuming you have no trouble with it, how would you describe your ease of solving this problem?FACSIMILEFACILE4I
12. SCAL IINS: In tis pbem, all but the fist lter, futh lter fom end, and lst two ltrs of ech wrd (oter tan thse arng in mth) hve ben roed.
Thre are two wals whch met at an anle of π/12. A bll is rled plel to one wll, and wll hit the oter. Amng tat the cins are pcly esic, cier how mny cins the bll wll hve wth the wals mod 10. Wat isct cold get in the way?
12. SPECIAL INSTRUCTIONS: In this problem, all but the first letter, fourth letter from end, and last two letters of each word (other than those appearing in math) have been removed. There are two walls which meet at an angle of π/12. A ball is rolled parallel to one wall, and will hit the other. Assuming that the collisions are perfectly elastic, consider how many collisions the ball will have with the walls mod 10. What insect could get in the way?MILLIONTHMOTH1M
13. SPECILA INSTRUCTIOLN: Li thli problle, tlh lals lettle lo ealc wolr (othle thla thols appeariln li malt) hla bele removle, thle hla bele insertle secoln lt lals.
Slilc grele folo (centerle la tlh origli) aloln tlh thrle planle x=y, y=z, aln z=x, thle couln tlh piecle. Whla li tlh bels folo lt uls?
13. SPECIAL INSTRUCTIONS: In this problem, the last letter of each word (other than those appearing in math) has been removed, then L has been inserted second to last. Slice a green food (centered at the origin) along the three planes x=y, y=z, and z=x, then count the pieces. What is the best food to use?PICKEDPICKLE6E

The indexed letters tell us that, in fact, Charlotte and Yuval weren't evil all along, and they just wanted us to have a RELAY GOOD TIME.