** The Bookmark **

Standard Sudoku and Spiral Galaxy rules apply - the numbers 1-9 appear once each in each row, column and 3x3 box, and every cell in the grid must belong to a galaxy. Galaxies have 180 degree rotational symmetry (in their shape, not their digits).

One of the digits from 1-9 acts as the centre for each galaxy. (E.g.: All the 1's act as the galaxy centres, making the numbers 2-9 *not* galaxy centres.)

A galaxy cannot have any cycles (a closed loop belonging to a galaxy) or cover any 2x2 region.

The sum of the digits in each and any tail around a galaxy must be equal. Digits may repeat within a tail. (To clarify, a tail is the string of cells that connects to the centre of its galaxy, not including the centre itself. Also, a 1x1 galaxy can be valid, having no tails at all.)

If *any* 5 or more cells along a row belong to the same galaxy, the digits in those cells must read across in ascending order. Finally, the digits in the two highlighted cells in the grid must also read across in ascending order.

Lösungscode: The nine-digit number read from Row 2.

**am 26. Juni 2020, 20:56 Uhr von Big Tiger**

Well, all right, if you say so. I can say for certain that figuring it out would not be my kind of fun, so I'll watch to see if anyone else does.

Zuletzt geändert am 25. Juli 2020, 02:10 Uhr

**am 26. Juni 2020, 10:10 Uhr von hamslice**

Now that Big Tiger has been convinced of the existence of a logical path to solve the puzzle, this comment has been edited to hide any and all hints.

Have fun trying to work this path out yourself!

Zuletzt geändert am 26. Juni 2020, 10:06 Uhr

**am 26. Juni 2020, 10:02 Uhr von stefliew**

I've found quite a few galaxy sets that can satisfy all constraints but one - the constraint regarding 5 or more cells needing to be read across in ascending order. Honestly, I am not entirely convinced that there is a single unique solution to this puzzle as I feel there may be another solution out there somewhere that also meets the conditions. This puzzle feels a lot like the setter came across a galaxy layout that he liked and shoehorned it into a puzzle without checking if there were any other possible solutions.

@hamslice I would like some assurance from you that you have done your best to ensure a unique solution to this puzzle, either through rigourous logical/mathematical proof or by computer-assisted brute-forcing. Your word that you have done so will suffice. I apologize for doubting you, but I cannot help but have my reservations. I don't want to waste time here and stumble upon an alternative solution by chance.

**am 26. Juni 2020, 09:31 Uhr von SirWoezel**

I can't even think of a way to put 9 180 degree rotational symmetric galaxies in the grid with the same, one-cell center number, that cover all of the cells in the grid.

I think figuring that out may lead to the solution very quickly as it will probably be some unique constellation.

**am 26. Juni 2020, 03:04 Uhr von Big Tiger**

What you've got here isn't so much a logic puzzle as it is just raw trial-and-error. There's no place to get started, no way to start ruling out certain numbers in certain spaces, no way to zero in on one square and say, "Okay, that has to be a 2". Even on some of the hardest puzzles on "Cracking the Cryptic", Simon and Mark are able to look at the clues and focus on a spot on the grid to get started.

I won't say this puzzle is completely impossible, but it's so far removed from a logical order of solving that I don't think you're going to find any takers on this site.

But you're welcome to prove me wrong. Where would you start? What logical path would you use to finally place the first digit on the grid?

**am 25. Juni 2020, 12:52 Uhr von hamslice**

Before anyone asks about the last paragraph in the rules - any really does mean any. Along a row, it could (for example) be the cells in columns 1, 4, 5, 6, and 9, and the 5 digits in those cells must be arranged in ascending order.