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We need to place the listed landmark locations into the supplied table. Counting the locations, there are 38, the same number of white spaces in the table, so it is reasonable to expect that one place goes in each white cell. But how to assign them?
Some research (probably using the Internet) will indicate that the places fall into groups based on what type of location they are: churches, parks, museums, universities, railway stations, and so on. Also, many of the places are in the same cities: Barcelona, London, Paris, Sydney, Tokyo. Altogether, we can identify seven different types of location, and eight different cities. This implies that the cities appear in columns of the table, while the location types appear across rows.
Now we can fill out the table, placing the city names in the top blue-shaded row. There are some ambiguities, as London, Sydney, and New York all have a Hyde Park, and Regent's is both the name of a park in London, and a university in London. But some trial and error reveals a consistent filling of the table (noting along the way that the cities are listed in alphabetical order, as a confirming indicator—but see also the puzzle designer's notes, below). Here we've also added the landmark type down the left side.
|Barcelona||London||New York||Paris||Rome||San Francisco||Sydney||Tokyo|
|Theatre||Akadèmia||Gymnase Marie Bell||Tordinona||Magic||Roslyn Packer||Imperial (Garden)|
|Metro Station||Horta||77th St||Opéra||Colosseo||16th St Mission||Martin Place||Shijō-mae|
|Church/Shrine||Sagrada Familia||St Patrick's||Sacré-Cœur||Santa Maria della Vittoria||Namiyoke Inari|
|Museum||Natural History||Pompidou||Children's Creativity||Victoria Barracks||Ōkura Shūkokan|
|House||Casa Vicens||10 Downing St||Villa Wolkonsky||Painted Ladies|
Next we have to make the intuitive leap that we should have a look at these locations on maps of the cities. If we do this, and then join the landmarks by tracing a line in the order reading down the table, we see that the locations in each city define the shape of a letter (click for larger maps):
The letters spell ALHAMBRA, the name of a famous landmark in Granada, Spain. This is the solution.
After this puzzle was released during the competition, a team wrote to inform us that the filling in of the grid was not unique. If you swap the columns for Barcelona/Rome, and Tokyo/Paris, while also swapping the rows University/Park, you can also complete the grid consistently. Furthermore, if you follow the subsequent mapping step, many of the results still give sensible looking letters, so it's not immediately obvious that this alternative is not the intended completion.
Unfortunately, none of us noticed this during construction or testing of the puzzle. By the time we were aware of it, it was too late, as several teams had been affected. This was basically our fault for not testing thoroughly enough, and our apologies go to the teams who lost points because of this confusion.
We take home the lesson that we cannot be too vigilant and careful during construction and testing to avoid unintended ambiguities. If there's a lesson for solvers, it's that we do strive to give helpful signs that you're on the right track. If you came up with both the possible grid completions, you should give more credence to the one where the cities are ordered alphabetically, since this is the sort of thing we deliberately construct into our puzzles to provide confirming signposts along the way.