I am looking for a specific building in Rome, Italy. To find it, follow these steps.
Fill the 12 small triangles in the gray area in the 6 large triangles.
Finish the 6 large triangles in a logical mathematical way, so they contain only integers
Convert to letters
Compress
Read
To start,
look at the given triangles. In each one, the number above each pair of cells is either the sum or the difference of the two cells below it.
This is consistent within each given triangle; there are six "sum triangles" (marked with a blue square below) and six "difference triangles" (marked with a red Δ).
We'll need to be consistent within each pair placed together. Looking at the top numbers, it looks pretty likely that the "sum triangles" will be placed in triangle 2, 4, and 5.
I'll start by placing those. It's a matter of trial and error to figure out which pair goes where.
The left-hand corners of the sum triangles are: 0, 1, 3, 6. The right-hand corners are 2, 1, 3.
For triangle 2, the 8 in the second row up must be made from 6 (from H or I) and 2 (from A, I, or K). This leaves five options to try. It turns out that A+H works.
For triangle 4, the 4 in the second row up must be made from 1 (from C or L) and 3 (from K). L+K works here.
For triangle 5, the only remaining 'sum triangles' are C and I.
The difference triangles are substantially easier to place.
The left-hand corners are 11, 22, 28, 37, 38, and 1.
The right-hand corners are 5, 23, 16, 21, 13, and 57.
For triangle 1, a difference of 35 can only be made from 57 - 22. This means J and D go there.
For triangle 3, a difference of 33 can only be made from 38 - 5. This means B and G go there.
For triangle 6, the only two remaining pieces to place are E and F.
So, the pieces are placed as shown here:
Now we "convert to letters". There are a lot of numbers between 1 and 26 here, so let's convert them with A1Z26:
The two central rows always contain letters. That looks promising! Of course, only one of the two could be 'controlled' by the puzzle setter, so only one row can be relevant... or at least, one row from each triangle.
The instructions say to "compress" the triangles. It turns out that (as noted by noneuclideanisms in the comments) one efficient way to do this is to turn every other one upside-down! Then they all fit together nicely:
Doing this spells out the answer across the fourth row: PALAZZO FUSCONI PIGHINI, a palace in the Regola district of Rome!
