Hell's Vampires
(Published on 26. February 2025, 10:23 by Andrewsarchus)
About:
- This puzzle was my gift to Nordy in the 2024 Secret Satan puzzle exchange. (like "Secret Santa", but with more diabolical puzzles). Nordy has enouraged me to share this puzzle here.
- This puzzle features a diabolical twist on Vampire Cells.
The Vampires in this puzzle behave a bit differently from Vampire Cells in other puzzles, so be sure to read the rules carefully.
Rules:
- Normal Regionless Sudoku (Latin Square) rules apply.
- Vampire Cells:
Vampire cells appear once in each row and column and form a complete set of the digits 1-9.
A vampire cell drains one cell in its surrounding 3x3 neighborhood, reducing the prey cell’s value to zero and increasing its own value by the amount drained.
Potential prey includes outside clues (even if they are invisible to the solver) and lower numbered vampire cells (lower original digit).
Vampires always select the highest valued eligible victim.
Vampire attacks are executed in ascending order of their digits.- First, the vampire containing the digit 1 attacks, then outside clues are recomputed using the new values of both vampire and prey.
- Outside clues which have been drained are NOT recomputed and remain at 0 forever.
- Next, the vampire containing the digit 2 attacks, and undrained outside clues are again recomputed.
- The process continues until the Head Vampire (containing the digit 9) attacks, and the grid is computed one last time.
- The grid seen by the solver represents the final state.
- X-Sums:
Except for the four corners, all outside cells, regardless of visibility, are
X-sums, which (until drained) contain the sum of values in the first X cells in the row/column from the clue's side of the grid, where X is the value in the first cell. The summing wraps around as needed for values of X larger than 9.
For example, if X=20, the entire row/column is summed twice to get to 18 cells, and then the first two cells are summed a 3rd time to get to 20 cells.
Example:
- 4x4 example is Sudoku rather than a Latin Square, but other than that, the ruleset is the same.
Play Online:
sudokupad: Hell's Vampires
Solution code: Digits in Row 3, left to right
Comments
on 27. February 2025, 10:34 by henrypijames
The break-in is at least ¾ of the solve LOL.
on 27. February 2025, 08:53 by Andrewsarchus
Added Example
on 27. February 2025, 08:25 by henrypijames
Am I understanding correctly that the vampire game starts with Round 0, i. e. before any vampire has acted, the outside clues are calculated using the original values of the inside digits.
Or, alternatively, does the game start with Round 1, i. e. all the outside clues are empty (value 0), and only after vampire #1 has acted, the first round of clue calculation is performed.
Your first statement is correct. The initial value of the clues are computed before the first vampire acts.
(see the example I added above)
--Andrewsarchus
on 27. February 2025, 04:34 by henrypijames
Yeah, I think it'd be good for the rules to state explicitly that:
Outside clues represent final values after every vampire has taken their turn, whereas inside cells retain the original digits before any vampire has acted.
I also suggest first explaining the overall process (vampires taking turns), and then how an individual vampire changes the grid. In the current order, when I read "(lower original digit)", I have no idea what it's talking about.
"Vampires always select the highest valued eligible victim" suggest there's always one single candidate victim with a higher value than all the others. Is this hidden negative constraint real? If not, how does a vampire choose between two candidate victims with equal value?
I'll provided some examples and clarifications later tonight. For now, the case of equal valued prey candidates, the solver would have to deduce which prey was chosen.
--Andrewsarchus
on 26. February 2025, 17:43 by Nordy
Without a doubt one of the coolest, funniest, and best puzzles I have EVER solved! This puzzle has an absolutely brilliant transition from “uhh this is impossible” to “wow this is incredibly elegant and awesome!” Once you understand the rules, the puzzle is remarkably smooth and indeed only 4 stars for difficulty, but I’ve rated it as 5 stars because internalizing the rules is no small feat! Thanks yet again for this diabolically wonderful gift
on 26. February 2025, 17:22 by gfoot
I'm not sure I understand "The grid seen by the solver represents the final state" - does this mean that I should enter 0 into cells that have been drained by nearby vampires, rather than entering their values from before they were drained?
No, as is typical of puzzles with modifiers, digits are different than values. Draining a cell inside the grid changes the value, not the digit.
Outside clues show values.
Inside the grid, however, the solver enters the digits which are not necessarily the same as the cell's current value.
Let me know if that helps. :-)
--Andrewsarchus
Thanks - I have solved it now, my confusion was the statement that the *grid* the solved sees is the final state, but I figured you really just meant the outside clues shown are the final states, and it solved nicely that way.
I don't think I actually used the top centre "24" clue, by the way!
on 26. February 2025, 11:32 by Chilly
Great idea, and lots of fun to solve. Not as tricky as it first appears once you internalise the rules, but like filuta said, a calculator might help most people at some point along the way.
on 26. February 2025, 10:38 by filuta
this whole idea and setup is just so cool and funny, at one or two points I really did resort to using a calculator though.
