Invisible Cages
(Published on 25. March 2021, 10:42 by Big Tiger)
Standard Sudoku Rules apply to the final numerical layout. Digits may not repeat on both long diagonals.
Digits within a Knight's Move of each other may not repeat.
Cages: The puzzle contains Killer Cages. Numbers in the corners indicate the sum of the digits in each cage, and no digit may repeat within a cage. However, the boundaries of the cages are invisible. For this puzzle, cages must include at least 2 cells (no single-cell cages are present); and numbers are placed as far left as possible in the top row of each cage.
The grid contains no 2x2 areas either outside the cages or within any single cage.
Finally, numbers outside the grid indicate the sum of all caged digits in the direction of the given arrow. Along diagonals, digits certainly may repeat when allowed.
*****
Setter's Notes :: March 25, 2021 :: Well, this was a bit of fun, he said sarcastically. I had to test it about four times because each time I did, I noticed that I took a mistaken leap without true logical backing on the test before. But I think I've got it now. Testing it that many times also allowed me to discover that two of the border arrows were never used, so I eliminated them.
If you're in the mood to leave a hidden comment about which digit you placed first, I'd be interested to know. I'd like to see if it's the same one I found first, as insight into how different solvers approach the same puzzle.
Solution code: Row 7, then Row 8
Comments
on 13. September 2024, 20:03 by obuibo11
The link is dead
BT: Duly noted! It's a VERY busy week for me but I'll replace that as soon as I can.
on 11. December 2023, 22:49 by Myxo
Neat puzzle! The penpa link is down, here is a SudokuPad link for anyone who wants it: https://tinyurl.com/yq6psv85
BT: Interesting ... do Penpa links expire after a time?
on 21. October 2021, 13:08 by cdwg2000
Very nice!
on 27. July 2021, 17:53 by Big Tiger
Wow - 100% and FIVE??? stars? I'm skeptical it will stay there but I'll enjoy it while it lasts, ha ha.
on 27. July 2021, 16:12 by Mody
Das hat enorm Spaß gemacht.
That was great fun.
*** Glad you enjoyed it!
on 31. May 2021, 10:23 by filuta
sorry, it is not apparent to me from the rules, whether the cages may intersect.
*** No, they may not. As with Killer Cages when you can see them, these cages do not overlap each other either despite being invisible.
on 2. April 2021, 13:07 by marcmees
one of the most satisfying solves so far. Even when breaking the puzzle a few times, it felt that interesting, with very nice twists, so I persevered. Thanks for this great puzzle.
*** That's high praise, indeed! Thank you! Glad you enjoyed.
on 27. March 2021, 21:58 by Sfayne
Great puzzle. I noticed by the end but I never used the diagonals rule, yet the logic path still seemed like it was flowing well
*** wow - in my novice/intermediate experience that strikes me as doing it the hard way, but ultimately getting the right arrangement of 81 digits is what matters! :-D
on 26. March 2021, 08:12 by MagnusJosefsson
Very nice! A little tricky in the beginning, flows easily after that.
on 26. March 2021, 07:51 by polar
Very enjoyable construction puzzle!
on 25. March 2021, 13:11 by Mark Sweep
Very nice! I enjoy these kind of sudokus a lot and loved the clever use of little killer clues in this one.
on 25. March 2021, 11:02 by Big Tiger
Added a sample image to clarify instructions for arrows.
on 25. March 2021, 10:50 by cdwg2000
What's mean "numbers outside the grid indicate the sum of all caged digits in the direction of the given arrow. Along diagonals, digits certainly may repeat when allowed."?
**** If an arrow pointing along a row said "20", then in that row, all digits within any cages would sum to 20. Along a diagonal, so long as all other rules are followed, digits might repeat.
******So there are some killer cages without a given sum, such as 45 in the second row? In addition, must the total number of killer cages be marked in the upper left corner? Can it only expand to the right and down?Because it is a 5-star question, I think the key rules need to be clarified. If there is a simple icon, it might be better, thank you!
***
Brian: Added an image just now. The arrows are NOT killer cages, but indicate the sum of all caged digits. If a digit is in any cage along the arrow's path, it is counted.
And the cage sum is in the top row of the cage, as far left as it can go. That still allows for a lower part of the cage to extend further left.
******It's ok，thanks.
