# Solution to Endgame Back to Puzzle

#### by Josh Alman, Yannick Yao, Anderson Wang, Rahul Sridhar, CJ Quines, and Jakob Weisblat

The endgame is both the final runaround and the capstone puzzle for the hunt, with the goal of locating an object that Professor Yew left behind in the perpendicular universe. Teams will need to gather measurement data from ⊥IW while Yew Labs researchers collect data from MIT. The measurement data from ⊥IW are minipuzzles related to the structure, navigational puzzles, or meta mechanics of each round:

AthleticsThe number of eggs to deliver times the number of goose tasks, plus the numbers of violet coins in space, legendary fish, and football routes.393There are 60 eggs, 6 goose tasks, 21 violet coins, 5 legendary fish, and 7 football routes, for 60*6+21+5+7=393.
StudentsThe product of the atomic numbers of Joshua and Anderson.272In the Student Center meta, Joshua and Anderson correspond to Sulfur (16) and Chlorine (17) respectively, for 16*17=272.
TunnelsThe number of ghost passages on the outside border times the number of skeletons (don't forget the meta!), plus the total number of ghost passages.201There are 11 ghosts passages on the outside and 36 passages in total (both can be counted on the map on the round page), and there are 15 skeletons (14 puzzles + 1 meta), for 11*15+36=201.
Yew LabsAUO SNTD UAALJIYL PUE PAJPUNY OML. Hmm, I think that may have gotten flipped...214Using the Yew Labs keyboard, we can rotate the message upside-down to get TWO HUNDRED AND THIRTEEN PLUS ONE, for 213+1=214.
Infinite CorridorThe number of the first puzzle with answer FINELY.160All the answers to Infinite Corridor puzzles can be found in Puzzle 73718, which shows that the first FINELY answer appears at Puzzle 160.
⊥IW.nano5 times the sum of the number of puzzle-giving kilotechnicians and the number of puzzle-giving milli bots.55There are 5 non-meta puzzles in ⊥IW.kilo and 6 non-meta puzzles in ⊥IW.milli, for 5*(5+6)=55.
Stata Center4 times the sum of the length of the paths in the room with a compass on the floor and the room mentioning “what you need is a sail".56The compass room has length 6 (SENSES) and the room for SAIL has length 8 (two for each letter in semaphore), for 4*(6+8)=56.
ClustersThe number you would get if the building 3 keypad said "145" and you then pressed "7".117Pressing “7” on building 3 keypad will sum the number of lit segments in “145” (which is 2+4+5=11) and append a 7 to the sum, which gives 117.
Green BuildingThe number you would get if you put "red green white" on a telephone.149The Green Building elevator buttons have red, green, white buttons on the 1, 4, 9 position of a telephone keypad, which gives 149.
Charles RiverThe three-digit number that would take the string "PLICAS" to the word "REPLICATE" (using only common words along the way).278The path is PLICAS -(2)> REPLICAS -(7)> REPLICATORS -(8)> REPLICATE, which gives 278.

When teams are collecting data from each location, Yew Labs researchers are also collecting measurements from the corresponding location at MIT.

RoundLocationMeasurement (in meters)
AthleticsEntrance to Z center (building W35)223
StudentsEast entrance to Student Center (building W20, right next to Anna’s Taqueria)222
TunnelsAccessible entrance to building 7 basement151
Yew LabsBeneath the walkway between building 9 and 33114
Infinite CorridorEntrance to the infinite corridor in Lobby 7 (right next to MIT seal)150
⊥IW.nanoNortheast corner of the exterior of MIT.nano (building 12)25
Stata CenterThe bottom of the ramp/stairs in front of Stata Center (building 32)16
ClustersNortheast corner of the exterior of building 5627
Green BuildingCenter of the Dot (the circular grass patch in front of Green Building/building 54)29
Charles RiverNortheast corner of Sailing Pavilion (building 51)198

These numbers are inconsistent with ⊥IW measurements, but they do match in the unit digit. Moreover, the 10 unit digits are exactly 0, 1, 2, …, 9, so we use that as an ordering, and use the difference (divided by 10) as an index into the corresponding round answers to get the cluephrase HYPOTENUSE.

Infinite CorridorHIRE A CONTRACTOR16015010H
TunnelsDECRYPT THEM20115150Y
StudentsSET UP AETHERNET27222250P
AthleticsTHREW THE GAME AND NOT THE BALL393223170O
Yew LabsTWO-D OR NOT TWO-D214114100T
⊥IW.nanoTHERE’S PLENTY OF ROOM AT THE BOTTOM552530E
Stata CenterIRON OUT THE INKS561640N
ClustersMETALINGUIST1172790U
Charles RiverLOB ROCK STAR27819880S
Green BuildingCLEAR ALL VINES14929120E

Upon discovering the cluephrase, teams are prompted to combine the measurements from the two universes using HYPOTENUSE. Since the measurements are from perpendicular universes, we should treat each pair of measurements as the two legs of a right triangle and find the hypotenuse of that triangle. We should also use the MIT locations where the measurements are taken along with these combined measurements to locate the object.

RoundCoordinates (approximate)Combined measurement (meters)
Athletics42.3584519, -71.0956365451.9
Students42.3589195, -71.0945403351.1
Tunnels42.3592440, -71.0934114251.4
Yew Labs42.3599143, -71.0936857242.5
Infinite Corridor42.3592657, -71.0929798219.3
⊥IW.nano42.3605263, -71.091498360.4
Stata Center42.3609782, -71.090790258.2
Clusters42.3609011, -71.0895246120.1
Green Building42.3599872, -71.0891299151.8
Charles River42.3586653, -71.0874820341.3

With these measurements, teams will be able to use various resources (e.g. Google Maps) to determine that the coin should be around building 16. As researchers approach the location, Professor Yew reveals that she had left a coin in a vending machine in building 16!