Totally Prime Sudoku
(Published on 21. October 2020, 19:35 by steelwool)
The coloured grid is symmetrical about column 5. Any coloured (killer) area has a mirrored pair and each coloured area may sum to a different prime number. All the possible coloured areas are shown, and the remaining (white) areas do not meet this constraint.
All the little killer diagonals that sum to a power of a prime number (which includes single diagonals at the corners) are shown.
All the sandwiches (between 1 and 9) that are either zero or sum to a power of a prime number are shown.
To clarify a couple of points.
- Powers of primes are not p^0=1.
- The white cells will not mirror as primes (which is not the same as saying that one does not contain a prime).
- Each coloured area has a prime sum, but the mirror may be the same prime sum, or it may not (they are both prime)
- A coloured area may have a repeating digit if it overlaps more than one Sudoku 3x3 box.
You can try this puzzle online by copying the url below.
https://tinyurl.com/yxceuol3
Solution code: Enter the digits from row 8 and column 3
Comments
on 29. October 2020, 19:17 by SudokuExplorer
Thanks for clarifying the rules, especially that they are not normal killer cages. Nice start which got a bit tricky at the end. Thanks for the puzzle :-)
on 29. October 2020, 12:28 by steelwool
clarify puzzle can repeat digits
on 29. October 2020, 12:27 by steelwool
clarify coloured areas can repeat digits
on 27. October 2020, 11:52 by Nylimb
The first time I tried this, I assumed that the white cells couldn't be primes, and quickly reached a contradiction. After that was clarified I tried again. At least twice I made mistakes and started over, but I finally got to the solution.
Thanks for the puzzle.
In the end I don't think I ever used the "white cells will not mirror as primes" restriction.
I think that one more clarification should be added to the description: A digit may be repeated in a colored cage; i.e. they're not normal killer sudoku cages.
@Nylimb well done. Agreed, thanks for pointing out about the killer areas, main comments updated now.
on 25. October 2020, 09:46 by steelwool
Added tinyurl link - thanks @tenaliraman
on 25. October 2020, 09:39 by steelwool
clarify the significance of the mirroring of the coloured areas.
on 22. October 2020, 15:00 by SudokuExplorer
@Luigi The little killer sums are powers of primes (when shown in the diagram)
@steelwool Does 1 count as a power of a prime (p^0)?
-- Hi, no, the powers are one and above - good question, a bit silly of me not to even think of it! The powers are always given, so a p just means 2,3,5,7. The killer areas are p, not p2 etc, so 17 but not 25. The little killer and sandwiches are p, p2, p3 or p4 as shown.
on 22. October 2020, 14:43 by Luigi
This cannot be a normal Sudoku.
In the last line 5 single primenumbers have to appear. There are only 2,3,5,7 available.
Hi, let me try to clarify. There are three single cells that are coloured in the last row, so these will be prime numbers. There are diagonals marked as prime (but those are not single cells, they are a sum along the whole diagonal). The white cells could have a single prime but not both - else they would be coloured. The blue areas at either end are four cells that count up to a prime number (but not necessarily the same sum). If you need any further hints, please ask. @steelwool
So what digits may appear in every row or column?
It's still a standard sudoku, 1-9 in each row, colour and 3x3 area.
on 21. October 2020, 21:05 by Nylimb
There aren't any thick lines dividing the grid into 3x3 boxes. Should we assume that normal sudoku rules apply anyway?
Yes, this is still normal sudoku in that every row, column and 3x3 area uses 1-9 once each.
on 21. October 2020, 20:20 by tenaliraman
Here is a tiny url for the puzzle:
https://tinyurl.com/yxceuol3
