mezzacotta Puzzle Competition 2016

Solution: 1D. Destinations

We need to place the listed landmark locations into the supplied table. Counting the locations, there are 37, 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
University		Regent's	Rockefeller		John Cabot		UTS	Keio
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
Park	Ciutadella	Hyde	Sheep Meadow	Tuileries			Tumbalong
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.

Puzzle design notes

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.