If this is were a valid sudoku, in the completed solution which ring contains the greater sum?

**Puzzle:**

In this puzzle, normal killer sudoku rules apply--fill each row column and box with the numbers 1-9, no repeats in cages, etc. The cage totals will need to be deduced. * Important:Each colored ring contains cages that all have the same total.*However, the totals may differ from ring to ring.

In addition, the sum of the numbers in each colored ring will appear in the circled cells.

It should go without saying, but I'll say it -- there's a nice logical straightforward solution path -- and no, it doesn't involve adding dozens of cells together.

If you like this one, you may want to try its reciprocal counterpart containing similiar but different logic in my Perfect Square Number Cages Sudoku Or you may try it's sequel: Rings Around the Rosy

Inspiration comes from multiple sources, including Phistomefel's Mystery Killer and Phillip Huber's Killer Sudoku which forced me to learn some grid geometrics.

This puzzle was featured on Cracking The Cryptic -- you can find that video here

Lösungscode: The sum of the red ring in the teaser, followed by column 8 from top to bottom.

Zuletzt geändert am 12. August 2020, 17:04 Uhr

Gelöst von Alphish, Madmahogany, randomperson1729, Greg, NikolaZ, henrypijames, MavericksJD, SudokuExplorer, zorant, SirWoezel, kishy72, Genomico, Jesper, mse326, Imperial Marcher, Narayana, Tojvoh, pdebruine, Nylimb, geronimo92, juventino188, MagnusJosefsson, MumboJumbo, marcmees, Philipp Huber, bosjo, polar, Mody, benjamin172, Bianca, bob, rimodech, risheek, boredduck

**am 5. September 2020, 17:30 Uhr von Mody**

Großartig

**am 23. August 2020, 17:37 Uhr von Philipp Huber**

Wow, I have only just now seen your mentions of my puzzle as an inspiration and had to put them on the top spots of my puzzles-to-solve-list.

Thank you very much for that!

Also, well done for creating a beautiful puzzle here. Both in theme as well as in the puzzling experience itself. I'm looking forward to trying your perfect squares sudoku as soon as possible! :)

**am 18. August 2020, 12:22 Uhr von marcmees**

wonderful sudoku experience

**am 12. August 2020, 17:04 Uhr von RockyRoer**

Added link to CTC video and Sequel Puzzle

**am 7. August 2020, 09:34 Uhr von Narayana**

I liked the Perfect Square Cages a lot but I must say this is another level. There is something that makes this one just more satisfying!

People should still try 0003U9 it needs more solves!

**am 7. August 2020, 04:01 Uhr von Genomico**

I was already wondering why that rating took so long. Well deserved one! :)

**am 5. August 2020, 15:39 Uhr von Genomico**

Beautifully constructed!

**am 31. Juli 2020, 18:53 Uhr von SudokuExplorer**

A masterpiece! You should definitely give this one a try. Even if you don't solve it, there are so many different ideas in the puzzle that it still will be an enjoyable experience.

Zuletzt geändert am 31. Juli 2020, 05:24 Uhr

**am 31. Juli 2020, 04:59 Uhr von RockyRoer**

@henrypijames what happens if R1C2 is 4?

you can add the digits in the rings in this sample if you'd like to convince yourself: https://f-puzzles.com/?id=y5lw8hn6

@henry I had tried making all three outer rings the same but unfortunately the geometry prevents that. I also tried making the outer two the same as the inner 5x5 square - all 105, but that was also impossible. It was quite satisfying studying the geometry/arithmetics and the inequalities required.

@everyone else: Let me know if you want help finding the sum of the rings easily -- I'm a math teacher and love explaining :-) Probably my last set puzzle for a while as school gets back into session soon.

Zuletzt geändert am 31. Juli 2020, 05:15 Uhr

**am 31. Juli 2020, 04:53 Uhr von henrypijames**

On the teaser question: Is it really possible, in any valid sudoku, for the purple ring sum to exceed the red ring sum?

Update: I wrote down some inequations and solved them. Seems possible - unless there's some hidden sudoku logic that prevents it.

**am 30. Juli 2020, 21:10 Uhr von MavericksJD**

Very nice one. Loved it

**am 29. Juli 2020, 23:00 Uhr von Madmahogany**

Wonderful logic, and a great use of some cell arithmetic.

**am 29. Juli 2020, 22:55 Uhr von Alphish**

This is spot-on!

I liked the variety of logic used here. I got stuck occasionally, but figuring out another step after that was very rewarding.

Well done! ^^

**am 29. Juli 2020, 22:47 Uhr von RockyRoer**

Fixed solution code. Fat fingers. :-)