Does Phistomefel's Ring Still Apply?
(Eingestellt am 23. Februar 2024, 08:43 Uhr von bodemeister)
I have provided some hints below in case you get stuck but still want to appreciate the rest of the solve.
Links: You can solve the puzzle here at CtC or here at Penpa.
Tracking cells are included to help disambiguate the doppelganger missing digits. Enjoy solving and please comment!
You can also check out my other puzzles here! Happy solving and please leave a comment if you enjoy the puzzle!
Rules:
- Doppelganger:
- Each row, column, and 3x3 box contains the digit 0 and eight of the nine digits from 1-9 (i.e. it's missing one digit that's not 0)
- Any two rows, any two columns, and any two boxes must be missing different digits
- For each 0 in the grid, the digits missing in its row, column, and box must be three different digits. - Killer: Digits in killer cages must sum to the number in the top left corner of the cage.
- Red Lines: The two digits on a red line are either equal or consecutive.
- Antiknight: Any two cells connected by a knight's move in chess must contain different digits.
Hints: Highlight white text to see the hint.
Hint #1: Color columns 1,2,8,9 and box 5 purple. Color rows 3,4,5,6,7 green. Purple and green each contain 5 zeros and 5 sets of the digits 1-9 with 5 digits missing. What is the greatest possible difference between the sums of digits in the green and purple sets?
Hint #2: Can the four corner squares of Phistomefel's ring contain a repeated digit?
Hint #3: Which digit is missing from box 5?
Hint #4: Can the digit 0 appear on the Phistomefel ring? Which digit goes in R5C5?
Hint #5: Why can't a large digit appear more then twice on Phistomefel's Ring?
Hint #6: Why can't a small digit appear twice in one of the outer 2x2 boxes?
Lösungscode: The missing digit in each column, from left to right.
Kommentare
am 24. März 2024, 01:58 Uhr von Kafkapharnaum
o_O I must say, I don’t even understand what I’m seeing right now haha -- how the heck did you find that XD I mean, I know you said you’d been thinking about doing something with the ring for a while, but still. I had noticed some things myself in my own puzzles, but would have never thought this could be usable, let alone shaped to that extent. In fact I went and checked almost all of my puzzles to compare and try and make sense of this, and NONE are anywhere close to similar to this, this is wild (and in fact, I think you’d get a kick out of Technodrome in that regard hehe). Well I love to see the ruleset not just used, but explored in new ways like this, that I could never ever have thought of or pulled off, that's for sure. Thanks so much! :D
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Thanks for giving this puzzle a go and for the overly kind words! I'm pretty happy with how it came together. I learned a lot while making it! I solved Technodrome on my phone on an airplane earlier this month and forgot to enter the solution. Will do now.
am 22. März 2024, 06:55 Uhr von bodemeister
Removed version 1 of the puzzle, and removed (version 2) from the name of this puzzle.
am 24. Februar 2024, 14:32 Uhr von wullemuus
The same concept and though different-really enjoyable to have two versions of this puzzle!
The different cages made it quite interesting to find the right digits as you promised this in your introduction. Well done!
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A nice surprise that you solved both puzzles! Thanks! I was kicking myself a little for publishing the first version, because it was the end of a holiday and I rushed myself a little, resulting in a puzzle that could have been improved.
am 24. Februar 2024, 08:49 Uhr von Mutx
Very difficult but somehow enjoyable... The logic is amazingly rigorous and lengthy, kudos!
For anyone attempting this, I recommend considering the missing digits as Schrödinger cells with an invisible number; its interaction with 0 would be much more straightforward.
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Hi Mutx, thanks for solving my puzzle, and congratulations for being the first one to solve this beast! That is an interesting idea about thinking of the missing digits as Schrodinger cells. I just used the tracking cells to extend the row, column, and box sizes to 10 to account for the missing digit, and of course to remember that the missing digits in columns 1,2,3 are the same missing digits in boxes 1,4,7, etc. Good solve, and thanks for your thoughtful comment!
