# Fill this Rangoli puzzle

I came up with this puzzle named Rangoli, which was a part of the Puzzle Ramayan, the qualifiers for Indian Puzzle Championship.

Rules

• Every cell must contain one of the four letters R, A, N, G.
• In each 2x2 box marked by bold lines, the four letters must appear once and read RANG in either the clockwise or anticlockwise direction.
• Cells with the same letter don't share an edge but can share the same corner.
• Each letter appears an equal number of times in each row and each column.

Example:

Solved example:

Can you solve this puzzle and show the intermediate steps?

First,

the letters diametrically opposite the givens can be filled.

Next,

there are two options for the directions. We can either have this...

...or the same picture, but with all red letters flipped to their opposites (R↔N, A↔G).

Using column 5 or 6, we can fill the top box:

And now we know this choice was correct; if we had to flip the reds, then the blue G in row 2 would touch a red G, rather than an A. This means we can update the guesses to certainty:

And now the rest of the puzzle is relatively easy.

Use column 3 or 4 to fill the other two boxes in those columns, then use rows 5-8 to fill the bottom left two boxes:

The top-right box needs an R in it, and one of the ways of placing that R conflicts. The rest is easily filled.

• Brilliantly done. Can you comment about the puzzle type, do you like it or not? Also, should the letters 'RANG' be replaced by something more neutral like ABCD or even 1234? Commented Jun 28, 2020 at 5:38
• @ABcDexter To be honest, I'm not a big fan. It seems like once the direction for the blocks is determined, it basically just becomes a Latin square puzzle. Because of how block directions work, a conflict on one half of a border between blocks always gives a conflict on the other side. So the letters and blocks don't really interact in an interesting way.
– Deusovi
Commented Jun 28, 2020 at 6:07
• In fact, it seems to me that the vast majority of the logic could be simplified: "Place a diagonal arrow in each 2x2 block, so in each column, half of the arrows point left and half point right; also, in each row, half point up and half point down. Adjacent arrows cannot be mirror-symmetric acros the border between them."
– Deusovi
Commented Jun 28, 2020 at 6:08
• Aah, I see. Thanks for your valuable feedback :) Commented Jun 28, 2020 at 6:12