This is a PERFECT sudoku puzzle.

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*** TODAY'S PUZZLE ***
We expected this sudoku to be good but it's actually exceptional. It's called 45-45-90 and it's from a debut constructor arctan. It was recommended to us by the brilliant constructor James Sinclair and we would like to thank him - give this a try, it's a blast!

Play the puzzle at the following link:

Rules:
Normal sudoku rules apply. Digits along an arrow sum to the digit in that arrow’s circle. Digits in yellow circles indicate how many yellow circles contain that digit. Additionally, digits in yellow circles must be grouped into pairs. Each pair form opposite corners of a square, one other corner of which must be the sum of the pair. (Eg if r4c7 and r7c4 were a pair, the sum could go in r4c4 or r7c7.) Different pairs cannot use the same square for their sum. (Eg if r3c4 and r4c3 were also a pair, then r4c4 could be used for the sum of this pair OR the sum of the previous pair, but NOT both.) It is possible that the sum for one pair of circles may itself be in a cell which is already circled. Which circles are paired and where their sums go must be determined by the solver.

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*** ROLLER COASTER NURIKABE by the_cogito ***

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▶ Contents Of This Video ◀

0:00 Theme music & Puzzle intro
1:04 Crossword video
1:30 Riffclown's Sudoku Hunt IS JUST OUT
2:03 Yesterday's video/puzzle
7:04 Happy Birthdays
9:20 Rules
14:10 Start of Solve: Let's Get Cracking

▶ Contact Us ◀

Twitter: @Cracking The Cryptic

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Simon Anthony & Mark Goodliffe
Box 102
56 Gloucester Road
London
SW7 4UB

(Please note to use our real names rather than 'Cracking The Cryptic'.)

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[christopheradams]

arctan here! thank you very much to simon for solving this, to james for recommending this, and to everybody for solving it! a few notes below:

--this is not my channel debut, technically, but it is my sudoku debut; i previously constructed the phistomefel ring crossword from september 2021.
--the rules for pairing the circles technically allow for the squares to not be aligned with the grid, which is not the intent; apologies for that. the original wording did explicitly rule that out, but that technicality crept in when trying to rewrite the rules to be briefer and easier to understand.
--apologies for no threes in the corner; as much as i wanted it to happen, the elegance of the sudoku had to come first.

[Skamba]

Rows 4-6 can only have two circled sixes because they're all in two boxes. Rows one and nine can't have any sixes. Therefore, the circle in row 8 must have a six. From there, the puzzle unfolds a lot faster than how Simon solved it.

[chrisjones]

Love that the creators name was arctan, and had a puzzle named 45-45-90

That in itself is as meta as the puzzle!

[Mephistahpheles]

@50:26 An obscure rule would help Simon: Black digits also count as digits.

[sjm]

I hope removing 2 from r2c7 doesn't lead to a problem

[BenCragg]

At the start of the solve, Simon erroneously removes a 2 from R2C7. Luckily, this can be resolved immediately by realising you need a 6 (1+2+3+4+5=15<16), and seeing where sixes can go - by row logic (and looking at boxes 4 and 6) you quickly find that you need a 6 in R8C5, that forces a 6 into R2C7. Problem solved. :)

[Gonzalo_Garcia_]

15:04 for me. Omg what a fantastic puzzle. The way everything suddenly falls into place is incredible. One of my favourite puzzles so far this year!!

[martysears]

A circles counting puzzle is always going to pique my curiosity, and this ruleset was an amazing twist on them. I agree with what Simon says at 20:45 - these are my absolute favourite types of puzzles to solve (and watch Simon solve) - the ones with meta deductions at the beginning - unwritten rules to discover, new logic to get your head round. This puzzle had all that good stuff. Absolute genius - creativity and innovation ooze out of this one

[abcde_]

I think there is a loophole in the rules. At 25:35 Simon deduces the corners of square (greens), but there is multiple other options to form squares if you don't assume that the square is alligned with the sudoku grid. For example, R2C7 and R3C4 could be the circle corners and then R1C5 and R4C6 would be one of the "sum" corners. Forming a slightly tilted, but still a valid square.

[Bittyfun]

I think that black 3 was my favourite digit in the puzzle. It was used in the logic of so many squares.

[mubutukinkeke]

Something I've noticed about these videos: Up until recently, Simon's video titles would capitalise the first letter of every word, including small connecting words (the, and, a, etc.), while Mark's video titles followed a more traditional method of capitalising just the important words, nouns and such. Interestingly, I've noticed that Simon's videos have begun capitalising nothing but the first letter of the title (with the exception of proper nouns and of course words capitalised for emphasis such as "PERFECT" in this particular video). I'm sure the conspiracy probably goes even deeper, and while I'm frightened of what I may unearth I believe it's for the good of all humanity that whatever cryptic message is being left by CTC is brought to light.

[stevezagieboylo]

Wow did Simon place those 6's the hard way (at 40:20 ish). Here was my reasoning:

There needs to be six 6's in circles, and there are only seven columns with circles.
Columns 4, 5, and 6 will support only two 6's total, so you will need to have a 6 in circles in each of columns 2, 3, 7, and 8. This places the 6 in column 8, which places the 6 in column 2, which places the 6 in columns 7 and 5, and then in columns 1 and 9 by sudoku. I had that in my first 8 minutes.

[markp]

18:31 finish. For my break-in, I looked at the columns. There are seven columns with circles, however only two of the same number will fit in the middle three columns (only circles in boxes 2/8). Therefore, you cannot use 7/8/9. You do need 6, to have enough digits to fill all circles. Since only two of them can go in columns 4/5/6, therefore columns 2/3/7/8 must have circled 6s. This places the 6 in column 8, which places the 6 in column 2, which leads to the 6s in boxes 3 and 8. The last two 6s (boxes 2/4) can be differentiated by considering the square rule. The 6s in r2c7 and r7c2 need opposite corners on the diagonal between the two, and therefore neither circle on that diagonal can be a 6. The other two circles in boxes 2/4 are the last two circled 6s. Since the maximum sum is 9, 6s have to pair with 1/2/3, and the 4s pair with themselves to make 8 sums. Since you have placed all of your circled 6s, the cells in r3c3 and r7c7 have to pair with each other, and must be 4s. Sudoku will place the other two 4s, and the square logic will identify all of the sum cells. From that point, it is basically classic sudoku, with a pair of short arrows thrown in.

An excellent puzzle; fun fun fun!

[clarityc]

Delightful! This is the sort of puzzle that has me kicking myself at the end in a joyful way -- I spent easily twenty minutes narrowing down my digits in circles, placing most of my sixes, parsing out the base logic, and not able to find a single break point past that, before I gave up and resorted to the video, only to discover that I'd forgotten a rule! (When you think the pairs of digits only have to be rectangles, not squares, the ruleset gets MUCH HARDER.) And then as soon as I knew that, because of all the groundwork I'd already done, everything else snapped into place immediately -- what fun! If only I'd paid attention to the puzzle name...

Thank you, arctan, for a lovely one.

[emilywilliams]

I usually don't read comments before writing my own, but for some reason I did skim a lot of them this time. I see that there was a quicker way to do something or other - but it is entirely OK with me that you did it the way you did, Simon. This also goes for proving something "the hard way" instead of some easier way. I love watching you solve, and even when you are not as efficient as possible, I feel that I learn something that I can apply to my own solving. I love it that you do not (neither you nor Mark) solve puzzles on video that you have already worked out a perfect solve path for. I far prefer that you do it cold, live, whatever you want to call it, even if that means that the solve is not a "best" solve. Your amazing brain is a privilege to watch in action. Thanks for this video.

[andrewmccullough]

When is a chocolate teapot not a chocolate teapot? When there is a green three staring at it. 51:10

[looweeg]

Ah Cracking the criptic with Simon. You guys have no idea how you help me go through my anxiety of the last few weeks. Getting better every day now, but you helped sooth me when it was at its worst.

[johngilbert]

It is stunning that this even resolves after all the circles are filled in. An amazing construct!

[rentalcustard]

28:55 for me. Normally I struggle with puzzles where you need to sit with a global constraint for a while before you can start to think about pencil-marks, but this one felt perfectly pitched in difficulty, and I loved how it fell into place after I managed to get started. Really really elegant!

[agitatorjr]

The break in for me was noticing that r7c7 couldn't be a 6 because then you could only place five 6s in the puzzle. Spotted it relatively quickly and from there it was an easy solve.