# Symmetries – a Quadritaisho puzzle

This is part 43 of the puzzle series Around the World in Many Days. Each part is solvable on its own.

Dear Puzzling,

This is a Quadritaisho puzzle. Divide the grid into rooms by drawing borders along grid lines. Each room contains exactly one symbol (circle, diamond, vertical bar, or horizontal bar). Rooms with a vertical bar | are symmetrical along an axis which runs vertically through the bar. Rooms with a horizontal bar are symmetrical along an axis which runs horizontally through the bar. Rooms with a circle ● are 180° rotationally symmetrical with the circle in the central point, and rooms with a diamond ◆ are 90° rotationally symmetrical with the diamond in the central point. Some symbols have a coloured background; in the finished grid, shade the entire room in the same colour as the background of its symbol.

I was actually meant to visit another destination before this one, but the plans have changed and this one was moved up instead. This is of course a completely plausible turn of events (as there are plenty of reasons one might have to deviate from the original plan during a round-the-world trip), and not at all an indicator of someone having been stuck trying to come up how to finish the next intended puzzle for the last three weeks... Anyway, today I have climbed quite a few steps to visit an extremely impressive religious site. Can you guess where I am?

Gladys will return in Escape from a Grand Canyon.

Solving the quadritaisho gives this solution:

Beastly Gerbil posted an answer shortly before mine with an explanation of how they determined the solution, so if you'd like to see that, check out their answer.

Now, notice that we have three colors: red, blue, and purple.

If we interpret purple as both red and blue, we can split the grid into two images, one red and one blue, as also seen in Beastly Gerbil's answer:

If we bring these two parts together, they look like this:

With some quick Google Lens-ing, we can identify these shapes as

• Ahh my lack of knowledge of Chinese has let me down, great job! I was staring at the first symbol thinking maybe it represented an statue of something :P Oct 24, 2023 at 14:43
• thanks! tbf, my knowledge of chinese only goes so far as being able to look at those shapes and identify them as chinese characters, but that certainly helped narrow down the google search results haha Oct 24, 2023 at 14:51

Partial: Can't quite work out the final location

Solving the grid:

1:

Simply filling in as many borders between shapes as possible to start (I'm sure I've missed plenty here), which is helped a lot due to a lot of adjacent colours requiring borders:

2:

Clean up any missed borders, and can start applying symmetry to some of the shapes.

3:

Same as last time, as more borders are placed it creates more obvious symmetries for other shapes.
We have an interesting situation bottom left, were the only fit for the bottom three left cells must be to a vertical bar creating a W shape.

At this point start shading in any rooms that aren't already fully shaded just to help visualise

4:

The grid is filling in nicely, we have some forced shapes at the top of the grid which domino down through the grid, in particular the circle top middle solves nicely:

5:

Some trickier final deductions, there are now some cells which can only be reached by certain shapes, in particular in the top left and bottom right. By considering these cells, we can place enough borders where everything finally falls into place (note I made an earlier mistake with a blue horizontal bar on the left earlier, which luckily became immediately apparent):

Now I think the next step:

Is to split the grid into two. Purple is the combination of red and blue, so if we separate the colours into two grids we get:

Which seems to be the right thing to do as it gives some distinct shapes, however my geography knowledge is poor and I can't quite decipher these

Will keep looking for the final answer, if anyone else finds it first feel free to post it as your own answer!

• Been going insane staring at the blue and red shapes for last half hour trying to find a pattern, so might need to give my eyes a rest! Oct 24, 2023 at 14:20
• Between steps 4 and 5, you swapped R8C3 from purple to blue... I don't know if that will affect your ability to swap patterns, however! Oct 24, 2023 at 14:39
• @acrabb3 good spot, not sure how that even happened as all the original cells were locked, I won't bother going back to change it now jucifer has solved though Oct 24, 2023 at 14:41