# Stostone - Aoi's Big Birthday

Rules of Stostone:

1. Shade exactly one stone, an orthogonally-connected group of cells, in each region.
2. No two stones in different regions are adjacent.
3. If a number is in a region, it tells the size of that region’s stone.
4. If you let the stones all fall down, they must cover exactly the bottom half of the grid.

The standard Stostone rules apply. The blue color is just for cosmetic purposes.

The example:

The puzzle (the full-resolution image can be found here):

This might be the biggest puzzle I've ever set. This puzzle celebrates the birthday of my OC (Original Character), Tenryuu Aoi, which I use as my profile picture, :). Special thanks to chaotic_iak and Nusi for testing the puzzle!

• Number 1 in the rules is not clear to me. No numbers in your puzzles - so 3 is not really useful. Interpreting your rules - shading according to 1 (need explanation for me) and 2 you create a 5 square deep rectangle?
– Moti
May 15 at 18:56
• @Moti Rule 1 means on each area (separated by bold lines) you must shade at least one cell, and all of the cells in a single area must be connected (and those shaded cells are then called a single stone.) Rule 3 is not useful in this particular puzzle, but the rule is there to complete the ruleset of the original puzzle type. And finally yes, if all stones are dropped, it must create exactly a 5x53 rectangles. May 15 at 23:21
• This is a very impressive puzzle! ...I have absolutely no idea how to break in to it.
– Deusovi
May 16 at 0:32
• Update: No, wait, I think I see something!
– Deusovi
May 16 at 0:37

Solution:

For such a marathon puzzle, it's impossible to post all details of the solution, so I'll just focus on some examples of the methods that I have used, and then some snap shots of my solving procedure.

In the beginning, I misunderstood the rule and thought that it suffices to have $$5$$ shaded cells on each column. It turns out that the rule means the "stones", i.e. connected cells, cannot break their form while dropping down.

Anyway, I started with the following kind of logic:

and I got stuck very soon. Note that at this stage I have basically broken the puzzle into two parts, left and right.

I then try to use the trial-and-error method. This seems to work much better, like this:

And after a while, I found that the left part had many possible solutions. I then came back and read the rules again and finally figured out what I was missing. This allowed me to continue with trial-and-error:

Now just some snap shots:

Left part completed. Despite the sizes, I found right part much easier than left part, but the reason could be that I got used to the method.

• Nice work! Is this the only solution?
– Moti
May 16 at 2:23
• @Moti Yes, if I didn't make any mistake, then it is the only solution. I have gone through all possible branches. May 16 at 2:36
• @WhatsUp Well done and great job! You spotted the break-in, which imho (and testers think) actually the hardest part :D. However, despite getting the final answer, the puzzle is solvable with pure logical paths and (sure enough) doesn't need any bifurcation; so it feels like this answer misses several interesting logics. I might wait for several hours for a more complete answer, otherwise I'm giving a checkmark for this. Once again, very well done! :D May 16 at 6:07
• I figured out the first steps quite fast but did use trial-and-error several times, in the form of "if this were X or O then it would force these cells and we would get a contradiction with the rules". Some are perhaps unnecessary as can be deduced in the reverse order, but I got a bit impatient then and just wanted to get it done. ちょっと遅いですが、お誕生日おめでとうございます。 May 16 at 11:54