Orange on Turquoise

Question

_{This is part 50 of the puzzle series Around the World in Many Days. Each part is solvable on its own.}

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Dear Puzzling,

This is a Beaches puzzle (or tricolour Aquariums, if you prefer). Shade some cells in the grid in red and blue. In every box marked with shaded borders, any white cells are above all blue cells, and any blue cells are above all red cells. (You can think of red as sand, blue as water and white as air.) Coloured numbers around the grid indicate the number of cells on that row or column with that colour.

Use the finished grid to find the name of my destination. I will not tell you how to fully interpret the grid, but will say that, with some simplification, Afghanistan would be the letter A, France the letter L, the European Union the letter N, Peru the letter U, Mongolia the letter X, and China a whitespace character.

Today I have visited a beautiful beach where orange-coloured rocks rim the turquoise waters. Can you guess where I am?

Love, Gladys.

Solve on Penpa+ (no answer check)

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Gladys will return in Winetasting Far from Home.

Answer 1

Gladys is ...

... at the Bay of Fires.

The Beaches puzzle

The final grid looks like this:



I have no partucular strategy for solving this. All cells on the same row within a region must be of the same colour. When a column or row has two coloured numbers, all three counts are known.

So let's look at the J shape in the left half. There are three red cells in column 3. The top cell can't be red, because there are only white and blue cells in the top row. The bottom row can't be red, because the single red cell in that row must go into one of columns 1 or 4. That means that the bottom three rows of the J are red. The top cell must be white, because there are no blue cells in that row and the red count for column 3 has already been used up.

The grid isn't large and similar reasoning plus some trying out will fill the grid.

The location

We are told how several countries and one organization correspond to characters. The correspondence is via the flags of these countries.

After removing crests, stars writing and other adornments, all of these flags can be considered as three vertical stripes of white, blue and red.

We probably need the 26 letters and we know that China is a whitespace character. And we have three different colours to work with: blue, white and red. That suggests three-digit numbers in a ternary number system, which can encode the numbers from 0 to 26.

The three digits are the colours: white = 0; blue = 1; red = 2. The number 26 = 222₃ is a space, the rest are letters from 0 = 000₃ (A) to 25 = 221₃ (Z).

The examples are:

= 000 = 0·9 + 0·3 + 0·1 = 0 → A

= 102 = 1·9 + 0·3 + 2·1 = 11 → L

= 111 = 1·9 + 1·3 + 1·1 = 13 → N

= 202 = 2·9 + 0·3 + 2·1 = 20 → U

= 212 = 2·9 + 1·3 + 2·1 = 23 → X

= 222 = 2·9 + 2·3 + 2·1 = 26 → space

Reading the solved grid from top to bottom, left to right, we get :

001 000 220 222 112 012 222 012 022 122 011 200
 B   A   Y   _   O   F   _   F   I   R   E   S