A prime example of the loneliest number
(Eingestellt am 25. Juli 2025, 19:34 Uhr von TheGreatGoatsbie)
Standard Sudoku rules apply.
Cells connected by an X must sum to 10.
Cells connected by an V must sum to 5.
Digits in a cage sum to the value in the corner of the cage.
Grey squares mark even digits.
Digits separated by a white dot must be consecutive.
Prime rules:
Place almost all primes under a 100 on the diagonals, so that they do not overlap. Double digit primes are read from left to right.
All primes under hundred have to at least appear once in these squares except primes made up out of two identical digits.
Prime numbers containing one or more prime digits may not touch each other orthogonally.
E.g. 29 and 73 may not share a border, but they may share a border with 89 because it doesn't contain a prime digit.
One is the loneliest number: Prime numbers made up out of two identical digits have ignored all the prime rules and do not form a proper pair.
For good measure here are the prime numbers between 0-100: 2/3/5/7/11/13/17/19/23/29/31/37/41/43/47/53/59/61/67/71/73/79/83/89/97 )"
Here are some examples of legal placement of some primes (read left to right). Pink shades break rules while the green ones don't. The number 5 in r1c1 should also be green.
Lösungscode: Row 3
Kommentare
am 2. August 2025, 21:23 Uhr von TheGreatGoatsbie
Reformulated the rules.
am 27. Juli 2025, 15:45 Uhr von Lackhand
I still don't understand the rules (the example contradicts my reading of them!)
Current text (ignoring some special cases & setup):
"""
Marked Prime numbers containing one or more prime digits may not touch each other orthogonally. ... The other prime numbers made up from non-prime numbers, can touch all other prime digits
"""
Region 3 of the example works the way I interpret these rules, with 43 and 89 adjacent and green (meaning a legal placement?).
Region 1 does NOT seem to match these rules, since 17 contains 1, which is not prime, therefore 17 should be allowed orthogonally adjacent to other marked cells.
However, it is marked pink (which I assume means rule counterexample due to coloring in region 9?).
Perhaps it is colored pink because 17 and 29 also appear in region 5 (as stated in the explanatory text).
But this is also a contradiction!
The text ("Note that the 17 and 29 in box 1 are also illegal because") contains the word "also"; therefore there is another reason it is pink.
More words might help. Perhaps the rule is that:
* The player must mark 21 pairs of diagonally adjacent cells and 4 individual cells
* The 25 prime values less than 100 must appear in these cells once each (their digits read left to right for the 2-digit primes)
* No prime digit in a marked cells may appear orthogonally adjacent to another prime digit in a marked cell. (This is a guess; I am not sure this is the intended rule!)
* There's something going on with 11 (specifically) that is even harder to capture with this ruleset. Potentially it forces is to read a diagonal 72 (etc) as 7 2 so that 1 1 can take some of the solo spots, though I can't be bothered to put that into terms of cells/marked cells/digits/values language ;)
Thank you for the construction, I look forward to mounting a second attempt!
am 27. Juli 2025, 15:11 Uhr von TheGreatGoatsbie
Revised some rules and added a better example. Im hesitating to put the puzzle on invisible since there is a lot to be desired and the concept is a lot cooler than the execution.
am 27. Juli 2025, 14:50 Uhr von TheGreatGoatsbie
Hi Lackhand,
I'm still reading your comment, but 17 is not allowed to be adjacent to other primes containing a prime digit because it contains a 7 which is a prime. Similarly, 29 is not allowed to be adjacent to another pcp (prime containing prime). That is why they are coloured pink. (the 7 and the 2 also border each other here.)
You are right in noting that my example is rather unclear because of the comment that it is 'also' illegal. I'm going to rectify that.
I see where your misunderstanding comes from, it is not the prime digits that aren't allowed to touch orthogonally but the prime numbers. e.g. 73 and 29 are not allowed to border one another.
The 11 is an outlier. Sadly it is not possible to fully place 11 on a diagonal because of the nature of the set up. It was kind of a riddle but since the ruleset is so convoluted that may be a bit much. I'll adjust that as well.
I hope this answers all your questions, thank you for taking the time.
I'll let you know when I've applied your comments.
am 26. Juli 2025, 00:06 Uhr von TheGreatGoatsbie
Added an example of correct prime placement
am 25. Juli 2025, 19:37 Uhr von TheGreatGoatsbie
Changed rule formatting
