Shroedinger's Hat
(Published on 22. March 2023, 18:16 by shadow-nexus)
We live in a world of quantum entanglement and quantum superposition, and so does this puzzle.
This can mess with intuition you previously gained from more classical systems. The differences may be small but
significant.
Just remember that Erwin Schroedinger suggested that the different terms of a superposition are "not
alternatives but all really happen simultaneously".
What does that mean?
Smart people like yourself might be able to figure that out.
Solve
Rules
| Sudoku 0-9 |
Fill the grid with the digits 0-9 so that no row/column/3x3box contains repeated digits.
No 3x3 box may contain its own box number. |
|---|---|
| Entanglement |
For each 0 in a 3x3 box, the box number of that box is placed in the same row in the leftmost column.
For each 0 in a 3x3 box, the box number of that box is placed in the same column in the bottom row. |
| Superposition | Cells containing a 0 are Schroedinger cells, representing a value of 0 or 10 (or both simultaneously). |
| Arrow | Values along an arrow sum to the value in its circle. |
| Thermometer | Grey paths are "quantum thermometers" on which each value is larger than the value directly preceding it on
that thermometer.
For thermometers having a single bulb, the direction of increase is away from the bulb and towards the tip(s). For thermometers having 2 bulbs or no bulbs, the direction of increase must be determined. Each grey path starting from the same bulb is a separate thermometer. |
| Kropki |
Cells separated by a white dot contain consecutive values.
Cells separated by a black dot contain values in a 1:2 ratio. Not all dots are given (i.e., there are no negative constraints). |
Notes/clarifications
In classical Sudoku each box is filled with the whole set of digits 1 to 9, but in this puzzle each box is "missing" one digit from 1 to 9 because it is replaced by 0. Be careful when "scanning boxes"!
The Schroedinger cells in this puzzle are not like those typically found in "10-in-9" puzzles. Each cell in this puzzle should in fact contain a single digit.
Boxes are numbered with the digits 1 to 9 in the order they appear in the grid, left to right then top to bottom, i.e.:
| 1 | 2 | 3 | |
| 4 | 5 | 6 | |
| 7 | 8 | 9 | |
When talking about this puzzle, I call the rows/columns of the 9x9 Sudoku grid as one would in classical sudoku:
with the numbers 1 to 9.
By extension, the leftmost column is "column 0".
The bottom row is "row 0" despite it being the last row, because in this puzzle 0 can represent 10.
Solution code: The first 20 digits in the grid (i.e., the first 2 rows).
Comments
on 29. January 2024, 03:47 by shadow-nexus
I added a Sudokupad link
on 27. March 2023, 15:48 by shadow-nexus
I rephrased the rules about thermometers to make it more clear that the "hat" consists of multiple thermometers, each with their own direction.
on 27. March 2023, 01:14 by Paquet Voleur
Wrapping my head around the thermo rule took me a while. Fortunately I was hitting a wall almost immediately so I wasn't spending a lot of time on a broken puzzle. Then I finally saw the hat as I needed to see it, that is, as four two-bulb thermos, and not as a complex four-bulb contraption with a single direction flow. After that progress finally started. An enjoyable puzzle and a very nice and impressive design!
RE: Thanks for your feedback! I'm glad you liked it!
I will try to rephrase the thermo rules to make that fact more clear.
on 24. March 2023, 15:41 by Briks
Beautiful design, no guessing necessary. Thumbs up!
RE: Thanks! I'm glad you enjoyed it!
