The Zodiac Project: Orrery
(Published on 14. January 2026, 07:17 by Nell Gwyn)
- Sudoku: Within the central 9x9 grid, place the digits 1 to 9 once each in every row, column and box.
- Irrwisch: All clues have had their digits replaced with letters or with question marks. Any two instances of the same letter (including in different clue types) must represent a different digit from 1 to 9 (an extra grid of cells has been provided for notetaking).
- A question mark may represent any digit from 0 to 9, and may represent the same number in different clues (a two-digit clue cannot start with a 0).
- Landvermessung: Shade some cells gray such that there are no closed orthogonally-connected loops of shaded cells (including 2x2s). In other words: for any two shaded cells, there can be at most one orthogonally-connected path of shaded cells between them.
- A circled clue in the grid gives the length of the shortest possible path that visits all shaded cells touching that corner (an infinity symbol [∞] means no such path exists, but that there is at least one shaded cell touching that corner).
- Japanese Sums: Clues to the left and above the grid give the sum of contiguous runs of shaded cells in the indicated row or column, in the listed order (adjacent sums must be separated by at least one unshaded cell).
- For each row and column, either all clues are given or none are, with the caveat that an asterisk ("*") represents any number of omitted clues, including no clues at all.
- Extra Region Path: The nine astronomical symbols in the grid must all contain nine different digits.
- In addition, there must be a path of shaded cells that visits all nine of them, in order from 1 to 9, without visiting any cell more than once.
NOTES
It took me two months after aqjhs nominated me to be the 27th setter in the Zodiac Project (all previous puzzles in the series can be found on the first puzzle's page, but, after much setting (and much testing), I made this! I will be nominating Zetamath to be the 28th setter in the series, and this will be their disjoint set:
Solution code: The shaded cells in rows 4 and 9
Comments
on 31. January 2026, 17:46 by Nell Gwyn
Clarified in the rules that the extra region path can't visit any cell more than once.
on 31. January 2026, 01:52 by Lyouke
Is my understanding that the path between astronomical symbols is allowed to double back on itself correct? i.e., the path between 2 and 3 is allowed to reuse cells from the path between 1 and 2. Or does "in order" mean no out of order paths are allowed?
EDIT: Unable to get proper headway, I was able to get the solution once I started working with the assumption that the extra region path must not cross the same cell more than once.
This is an excellent puzzle, once it got going it flowed beautifully to the end. It's a shame it took so long for me to do it, doesn't work too nice on mobile with how big the grid is.
on 21. January 2026, 02:13 by Sotehr
A wonderful addition to the series!
on 15. January 2026, 16:24 by Sangens
I have a question on the Infinity symbols. If just one of the four cells is shaded, would the path be of length one?
~ ~ ~
Correct. - NG
on 14. January 2026, 19:16 by ChinStrap
Beautiful and only slightly brutal. Really enjoyed testing.
on 14. January 2026, 18:38 by aqjhs
amazing use of the geometry of the extra region! <3
on 14. January 2026, 14:47 by Christounet
I already have the first deduction of zetamath's puzzle ;)
Your puzzle looks really cool btw, look forward to trying it soon!
