## Solution to A Puzzle with the Answer YOUKILIS

Author: Chieu Nguyen

The puzzle consists of 16 flights, each between two airports indicated by their 3-letter IATA codes, along with a distance in kilometers. If sorted by the first airport code (as is given), then the first letter of the second airport in each pair forms part of a message: these spell out ANSWER IS YOUKILIS.

In four of the flights, the distance given is exactly the great circle distance between the two airports, but in the others, the distance given is much shorter than the real distance ... it is actually half the circumference of the Earth minus the real distance. In the pairs where there is a discrepancy, the two distances add up to about 20,000 km; there is some variation here because the Earth is not exactly a sphere and is slightly wider than it is tall.

 IATA code Location Latitude Longitude Actual distance (km) Given distance (km) BLT Blackwater, Australia 23.60° S 148.81° E 16069 3942 ASI Georgetown, St Helena, Ascension and Tristan da Cunha 7.97° S 14.39° W CFG Cienfuegos, Cuba 22.15° N 80.41° W 1459 1459 NOB Nosara, Costa Rica 9.98° N 85.65° W DJB Jambi, Indonesia 1.64° S 103.64° E 17665 2340 SNU Santa Clara, Cuba 22.49° N 79.94° W DOH Doha, Qatar 25.26° N 51.57° E 4776 4776 WAM Ambatondrazaka, Madagascar 17.80° S 48.43° E DOP Dolpa, Nepal 28.99° N 82.82° E 16337 3689 EZE Ezeiza, Argentina 34.82° S 58.54° W GVR Governador Valadares, Brazil 18.90° S 41.98° W 15138 4869 ROK Rockhampton, Australia 23.38° S 150.48° E KDM Kaadedhdhoo, Maldives 0.49° N 73.00° E 17041 2963 IPC Hanga Roa, Chile 27.16° S 109.42° W KHW Khwai River Lodge, Botswana 19.15° S 23.79° E 3185 3185 SRH Sarh, Chad 9.14° N 18.37° E MAO Manaus, Brazil 3.04° S 60.05° W 16162 3846 YGJ Yonago, Japan 35.49° N 133.24° E NAW Narathiwat, Thailand 6.52° N 101.74° E 5478 5478 OHE Mohe, China 52.91° N 122.43° E PIU Piura, Peru 5.21° S 80.62° W 15562 4444 URC Ürümqi, China 43.91° N 87.47° E PMR Palmerston North, New Zealand 40.32° S 175.62° E 16628 3379 KAN Kano, Nigeria 12.05° N 8.52° E SHC Shire, Ethiopia 14.08° N 38.27° E 15995 4013 ITO Hilo, United States 19.72° N 155.05° W TND Trinidad, Cuba 21.79° N 80.00° W 18578 1455 LEA Exmouth, Australia 22.24° S 114.09° E TWU Tawau, Malaysia 4.31° N 118.12° E 17271 2760 IOS Ilhéus, Brazil 14.82° S 39.03° W XMH Manihi, French Polynesia 14.44° S 146.07° W 16111 3900 SMS Sainte Marie, Madagascar 17.09° S 49.82° E

This suggests that the flights are not connecting points on the surface of the real spherical Earth but rather on the surface of an alternate Earth that is topologically a projective plane (also hinted in the flavortext), specifically the one where every point on the surface of the real Earth is equated with its antipode, the point on the opposite side.

Plotting these paths on a map of the alternate Earth yields a message, seen here in an azimuthal-equidistant projection:

It is also possible to plot the paths on the surface of the real Earth, but replacing points with antipodes so that all the paths end up on the same hemisphere, or to plot two paths for every path, one on each hemisphere.

Since there is no inherent orientation to the projective-plane Earth, there is an additional arrow to confirm the message, due to the possibility of reading it upside-down, flipped, and/or out of order. The intended message (and the title of the puzzle) is MIAMI, and the arrow points roughly to the city of Miami, Florida, United States.