# Solution to Level One

#### by Curtis Chou, Azalea Weisblat, Jon Schneider, Lewis Chen, Rahul Sridhar, Anderson Wang, Yannick Yao

The ⊥IW.nano round had a peculiar unlocking structure. When solvers first opened the round, it was entitled ⊥IW.giga and the metapuzzle for that round—Rule of Three—was already solved. Solvers needed to determine that one of the puzzles in the round—Twins—was impossible to solve normally and must be backsolved from the meta. When this puzzle was backsolved, the website allowed solvers to “zoom in” to ⊥IW.kilo, a whole new round with Twins as the metapuzzle. Solvers then needed to repeat this process and backsolve a particular puzzle in ⊥IW.kilo to enter ⊥IW.milli. Finally, in ⊥IW.milli, solvers found that one of the individual puzzles was titled ⊥IW.nano. Backsolving ⊥IW.nano completed the entire round and fixed the ⊥IW.nano building.

The answer to this puzzle is a feeder to Twins—the metapuzzle of ⊥IW.kilo. We know Twins has the answer GLOBE. As stated above, we must reverse-engineer how Twins worked and use that information to backsolve this puzzle.

The other answers in this round are:

```BUMBLE
MANIAC
OREO O'S
ORSINO
```

The image on the Twins meta page has a series of directional signs with blanks on them attached to flagpoles. On each pair of signs on a flagpole, six of the blanks on the signs are labelled with the numbers 1 through 6. If we fill in these six blanks with the six letters of a particular answer in this round, we’ll find that we can fill in the rest of the blanks on each sign to yield a city name:

BUMBLE1???56??? / ?234??BETHLEHEM3200 kmMUMBAI5700 km
MANIAC1?3???4??? / ?2?5?6??MONTEVIDEO1600 kmDAMASCUS10800 km
ORSINO??2?45 / 13?6BERLIN500 kmOSLO1100 km
OREO O'S?1??4?6? / ?23?5???TOULOUSE2300 kmPRETORIA8500 km
?????12? 5???? / 34???62700 km4600 km

The two flags on the poles don’t match either of the two cities filled in on the signs. The key at this point is to realize that these pairs of cities have one sister city/twin town in common, and that that city is the distance away given on the signs and is in the country given by the flags. For example, Saint Petersburg is in Russia and is approximately 3200 km away from its sister city Bethlehem and 5700 km away from its sister city Mumbai.

BUMBLE1???56??? / ?234??BETHLEHEMMUMBAISaint PetersburgG
MANIAC1?3???4??? / ?2?5?6??MONTEVIDEODAMASCUSSão PauloL
ORSINO??2?45 / 13?6BERLINOSLOWarsawO
OREO O'S?1??4?6? / ?23?5???TOULOUSEPRETORIAKievB
?????12? 5???? / 34???6E

Now, in order to backsolve, we must determine how to get the letters GLOBE from these rows. The fact that there are two flags hanging from each pole give us a hint as to how to do that; we can plot the lines between each sister city pair on a map and read out the result as semaphore. For example, you head due south from Saint Petersburg to get to Bethlehem, and due southwest to get to Mumbai. This corresponds to the semaphore letter G.

Bethlehem (TLV) - Saint Petersburg (LED) - Mumbai (BOM) = G
Montevideo (MVD) - São Paulo (SAO) - Damascus (DAM) = L
Berlin (TXL) - Warsaw (WAW) - Oslo (OSL) = O
Toulouse (TLS) - Kiev (KBP) - Pretoria (PRY) = B

The diagrams above were produced by a great circle mapping tool, and the cities are marked by the airport code of their closest airport.

Now we can begin backsolving the answer to Level One. Based on the last remaining flagpole, we know that it corresponds to a city in the United States with sister cities approximately 2700 km in one direction and 4600 km in another. Because we know this city must extract to the semaphore letter E in GLOBE, we know that one of the sister cities is to the south and the other is to the northeast.

The harder of these two criteria to meet is having a sister city several thousand kilometers to the northeast. Most of the U.S. has either largely unpopulated areas of Canada or the Atlantic Ocean in this direction and at this distance. However, there are a few options in the North Atlantic for 4600 km.

In the above diagram, the area between the southern pair of lines corresponds to places that are the appropriate distance from Iceland, and the northern pair correspond to Ireland.

Iceland has many sister cities but almost all of them are in Scandinavia. However, none of the sister cities in the U.S. fits the enumeration or is in the appropriate geographic band.

So it must be a city in New England matching a city in Ireland.

Further reasoning along these lines might lead us to look at well-known six-letter cities in Ireland and examine their sister cities, but clever solvers might skip this step. In the ⊥IW.giga round, we “zoomed in” from a puzzle about the solar system to an answer corresponding to the Earth. In this ⊥IW.kilo round, then, it makes sense to “zoom in” further to an answer corresponding to Cambridge, MA, where MIT is located.

As it happens, Cambridge, MA has a six-letter sister city in Ireland, GALWAY, and a sister city in Haiti with the appropriate enumeration, LES CAYES. Taking the letters from the appropriate positions in these cities gives the answer LEGACY.