Test of the Alchemist’s Rune

The Test of the Alchemist’s Rune

A great discovery from Tyana! A series of ancient tablets, inspired by Thoth himself, have been unearthed. If deciphered, these tablets could reveal the secrets of the philosopher's stone and life itself. Unfortunately, the text is so cryptic, that even the hieroglyphs themselves were not written down, but are obscured by a numeric code. Mastering this code is the first step to discovering the secrets that Thoth graced our ancestors with.

Summary

An Alchemist's Rune (More commonly known as a nonogram) is a 10x10 square grid with numbers along the left and upper edges indicating how many squares in that row of column need to be filled in. Individual numbers indicate how many of those squares need to be adjacent to each other, while a comma indicates that there is a gap of any number of spaces.

Setup

The rune designer is given a 10 x 10 grid to work on. Clicking within a square colors it in, clicking again makes it blank. After creating their desired image, the puzzle can be opened to the public.

Note, it is entirely possible that any particular rune might have multiple valid solutions! Hence, being able to finish and judge a puzzle should rely on filling in the grid in such a fashion that it meets the requirements, even if that does not match the designers initial layout.

Examples

If a row is preceded by 3, 2, 3 then in that row there must be three adjacent squares filled in, a gap of any length, two adjacent squares filled in, a gap of any length, then three adjacent squarest filled in. Since a row is 10 squares long, the only possible solution for that row is XXX_XX_XXX.

If the numbers were instead 2, 2, 3, then 4 solutions are possible.
1) _XX_XX_XXX
2) XX__XX_XXX
3) XX_XX__XXX
4) XX_XX_XXX_
You would need to use information from other rows and columns to see what would fit.

A blank rune would look something like the following,

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3
4
1,2,1
6
4
4
4
1, 1, 2, 1, 1

We'll begin by filling in the bottom row, which has only one possible configuration.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3
4
1,2,1
6
4
4
4
1, 1, 2, 1, 1	X		X		X	X		X		X

Next, we can do the two center columns. We know that they contain seven adjacent filled cells which include the bottom two.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3
4					X	X
1,2,1					X	X
6					X	X
4					X	X
4					X	X
4					X	X
1, 1, 2, 1, 1	X		X		X	X		X		X

The rest of the cells in those columns are blank. The third row contains two sets of three adjacent cells, and we don't know exactly what cells those are yet, but we do know that those cells must include columns 2, 3, 8 and 9.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3		X	X					X	X
4					X	X
1,2,1					X	X
6					X	X
4					X	X
4					X	X
4					X	X
1, 1, 2, 1, 1	X		X		X	X		X		X

Those are the only squares which can be filled in for columns 2 and 9. That leaves only one possibility for row 6.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3		X	X					X	X
4					X	X
1,2,1					X	X
6			X	X	X	X	X	X
4					X	X
4					X	X
4					X	X
1, 1, 2, 1, 1	X		X		X	X		X		X

Now look at row 5. By process of elimination, the individual squares filled in must be columns 3 and 8. It can't be column 1 or 10 since those columns are known to have two adjacent squares being the filled in cells closes to the top. Column 1 or 10 of row 4 or 6 can't be filled in. We also know that columns 2 and 9 are complete. It can't be column 4 or 7 since that would put the filled in cells adjacent to the two we already have filled in.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3		X	X					X	X
4					X	X
1,2,1			X		X	X		X
6			X	X	X	X	X	X
4					X	X
4					X	X
4					X	X
1, 1, 2, 1, 1	X		X		X	X		X		X

Columns 3 and 8 are complete, no more cells can be filled in for those columns. That makes Rows 4, 7, 8 and 9 straightforward, followed by columns 4 and 7.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1
1,1
3,3		X	X	X			X	X	X
4				X	X	X	X
1,2,1			X		X	X		X
6			X	X	X	X	X	X
4				X	X	X	X
4				X	X	X	X
4				X	X	X	X
1, 1, 2, 1, 1	X		X		X	X		X		X

Just the first two rows and it's complete.

	2, 1	1	1, 2, 1	2, 4	7	7	2, 4	1, 2, 1	1	2, 1
1,1	X									X
1,1	X									X
3,3		X	X	X			X	X	X
4				X	X	X	X
1,2,1			X		X	X		X
6			X	X	X	X	X	X
4				X	X	X	X
4				X	X	X	X
4				X	X	X	X
1, 1, 2, 1, 1	X		X		X	X		X		X

By Apis, it's a bull!

Construction Cost Suggestion

This test is probably most similar to Pathmaker or Hexaglyphs in terms of thought processes required, and construction costs could be of similar nature. Wire made of some sort of alloy to form the grid, canvas for a background, black raeli tiles as playing pieces. Since the flavour text makes oblique reference to the Emerald Tablet, construction requirements of variously sized Emeralds, Cut Jade, or even Green Sun Marble might be suitable.