Vampire Chromodynamics
(Published on 2. March 2025, 23:36 by Andrewsarchus)
About:
-
This puzzle is the first in a series that will include three types of modifier cells:
Schrödinger Cells, Doublers, and Vampires.
Rules, including those for the modifiers, may differ slightly for each puzzle in the series, so read them carefully.
Rules:
- Each row, column, and box contains the digits 0-9 once each.
In order to accommodate ten digits in nine cells, one cell in each row, column, and box is a Schrödinger cell (s-cell for short), which contains two digits. - In addition to s-cells, this puzzle also contains vampire cells and doublers...
One cell in every row, column, and box is a doubler.
One cell in every row, column, and box is a vampire.
Doublers, vampires, and s-cells may not overlap. Each cell can be at most one of these.
Doublers and s-cells, however, may fall prey to vampires cells.
Each doubler cell contains a distinct digit from 0-9.
Each vampire cell contains a distinct digit from 0-9.
S-cells are not similarly constrained, and two or more s-cells may contain the same pair of digits.
(Note, that with 10 digits, and only 9 of each modifier type, there will be one digit left out of the doublers, and one digit left out of the vampire cells.) - The value of a doubler is twice its digit, but this value can be transferred to a vampire cell which preys upon it, reducing the doubler's value to 0.
- The digits in an s-cell are coordinate pairs.
The value of an s-cell with digits A and B, such that B>A, is the same as the value of the cell in Row A, Column B, where cells in Row 0 are Numbered Rooms clues (see Numbered Rooms rules below).
Cells referenced by an s-cell's coordinates may be of any type, including other s-cells, but an s-cell may not reference itself, nor may it reference a cell which would create a circular dependency.
An s-cell may also be preyed upon by vampire cells, in which case the s-cell's value is transferred to the vampire cell, reducing the s-cell's value to 0. The cell referenced by the s-cell is unaffected. - Each vampire cell preys upon one of the cells in its surrounding 3x3 neighborhood.
Vampires may not prey on each other, and each prey cell can only be preyed upon by one vampire (no sharing prey).
The value of the prey cell is added to the vampire cell's value, and the prey cell's value is then reduced to 0.
Note that when vampires prey upon s-cells, they must avoid creating circular dependencies. For example, an s-cell which references a vampire cell cannot be preyed upon by that same vampire cell (but could be preyed upon be a different vampire cell as long as a circular dependency is not created). - Modifier Column Indexers:
The cells in Column 2 index the position of Doublers in their row.
The cells in Column 5 index the position of S-cells in their row.
The cells in Column 8 index the position of Vampire cells in their row.
The Indexer cell's VALUE is the column in which the indexed cell occurs.
VALUEs of indexer cells are not permitted to reference cells beyond the edge of the grid.
In other words, indexer cell values may differ from their digit(s), but must still be in the range 1 to 9. - Diamonds separate cells with values which sum to the number in the diamond.
- Equal Signs separate cells with equal value.
Not all possible equal signs have been given. - Dagger symbols in a cell, indicate that the value of the cell matches the number of all prey cells in its row and column combined.
All possible daggers have been given. - Numbered Rooms: In this puzzle, numbered room clues are invisible, and only exist in cells in Row 0 that are referenced by one or more s-cells somewhere in th grid.
The value of the numbered rooms clue is the DIGIT in the in the Nth cell from the clue, which is not necessarily the same as the value of the Nth cell.
To avoid ambiguity, the Nth cell may NOT be an s-cell, but can be a doubler, vampire, or prey cell.
The value N is the digit in the 1st cell seen by the clue, which must not be a modifier, nor a prey cell.
(Note this requirement does not apply to columns which do not have a numbered rooms clue)
Example:
let R5C2 be a doubled 9, with value=18
let R1C2 be a 5
let R7C7 be an s-cell with digits 0,2
The s-cell references R0C2, so there is a numbered rooms clue there. N = R1C2 = 5, so the value of the clue is 9 (the digit of R5C2, not the value which is 18).
Thus the value of R7C7 is 9 (unless it is preyed upon by a vampire, which adds the 9 to its own value and reduces the s-cell value to 0 - note this does not change the value of the numbered rooms clue, which is still 9).
Multiple s-cells may reference the same clue.
Examples
- vampire / s-cell / prey interactions
- numbered rooms examples
Play Online:
sudokupad: Vampire Chromodynamics
Solution code: Values (not digits) in Row 4, left to right
Comments
on 4. March 2025, 05:50 by Andrewsarchus
added examples
on 3. March 2025, 16:41 by henrypijames
So I did understand the rules wrong. Because I was talking about a different scenario (and thinking that you had been talking about it too), namely when the prey is not itself an s-cell, but a target referenced by an s-cell:
What happens if V preys on C, and S references C? C obviously has a value of 0, what value does S have? The rules say a cell can only be one of vampire, doubler, and s-cell, but it doesn't rule out a cell from being prey and target at the same time.
Your original phrasing "unaffected by this" is unclear because "this" could refer to many different parallels.
The s-cell referencing a prey cell will have a value of 0.
(example images added)
--Andrewsarchus
on 3. March 2025, 07:19 by henrypijames
It seems quite impossible to maintain the whole ruleset in my head, let alone having any bandwidth left for solving the puzzle ...
"The cell referenced by the s-cell is unaffected by this." Does this mean that a shell referencing a prey cell does not have a value of 0, but the same value the prey is transferring to its vampire?
Example images added
--Andrewsarchus
