Apsidal Precession (Black Hole)
(Published on 14. October 2025, 04:11 by gdc)
This puzzle uses the Black Holes ruleset by heliopolix. It's quite a mouthful, but offers some unique geometric logic with modifiers that I wanted to try ot for a while - and I finally did! Thanks heliopolix, Mad-Tyas, ChinStrap, Black_Doom, aqjhs and jakestilesowen for testing. Hope you enjoy!
Black Holes (Nullifiers): Place nine black holes, one in each row, column, and box. Digits may not repeat on black holes. For the purposes of the clues, black holes have a value of zero.
White Holes (Doublers): Place nine white holes, one in each row, column, and box. Digits may not repeat on white holes. For the purposes of the clues, white holes double the value of a cell.
White holes and black holes never share the same cell.
Killer Cages: Digits in cages cannot repeat (though values can). Values within a cage sum to the clue in the top left. A killer cage must contain an equal number of black and white holes, but that number may be zero.
Teleporting Little Killers: Clues outside the grid with arrows give the sum of digits along a diagonally-traveling path starting in the cell pointed at by the arrow. This path only ends when it reaches an edge of the grid. When the path enters a black hole cell it teleports to the white hole cell with the same digit maintaining the direction of travel of the original path and including the value of both holes in its sum. The path must visit the same number of black and white holes, but that number may be zero.
Hole Sandwiches: Clues outside the grid without arrows give the sum of the digits between the holes in the row or column, not including the holes.
Example
Want To Solve More Black Holes?
Check out Intro to Black Holes, Part I and the puzzles linked there to see how the creator of the ruleset uses it. The intro series gives a very gentle entry and the advanced series contains incredibly beautiful and creative applications involving Schrödinger cells!
Solution code: The bottom row (row 9) left to right (9 digits)
Comments
on 17. October 2025, 22:11 by ViKingPrime
I don't know what about this puzzle in particular brought about the hole pun thing but I'm a fan.
on 15. October 2025, 15:36 by Franjo
The terrible 108 nearly left me lost in desperation! Thank you very much for creating and sharing this great puzzle.
on 15. October 2025, 00:37 by eladv
Whow, that was hard! And great! It's one of those great solved, where I spent the first 40 minutes kind of staring at the screen not figuring out what to do, and then it all started to come together, and in retrospect it's really all obvious. Beautiful puzzle.
on 14. October 2025, 19:07 by aqjhs
this was my 800th solve :D
on 14. October 2025, 17:32 by jakestilesowen
This is a great puzzle and a great intro to the black hole ruleset. Thanks for it!
on 14. October 2025, 16:50 by heliopolix
This puzzle gives the (w)hole experience! There are tons of delightful steps along the way.
Thanks for setting!
on 14. October 2025, 12:46 by lmdemasi
Hole-y mole-y
on 14. October 2025, 12:29 by Black_Doom
Lots of fun, very cool logic
on 14. October 2025, 07:29 by JeremiahHowden
Despite being my first time with this ruleset, this puzzle managed to be approachable yet still quite challenging. Finished just under 90 minutes. Really satisfying logic all around. Another excellent puzzle gdc, thank you.
