Inner Peas

Normal sudoku rules apply. Shade some cells so that all shaded cells are orthogonally connected, and all unshaded cells are orthogonally connected. No 2x2 region can be completely shaded or unshaded. Each cell in one region has a value of its digit plus 1. Each cell in the other region has a value of its digit minus 1.
The sum of the values of cells on lines connecting two circles is equal to a concatenation of the two values in the circles, in some order. For example, 3_346_1 is valid, as 3+4+6=13. Leading zeros are allowed. Every line between two circles is summed separately.

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Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships. We're also "cryptic crossword" aficionados. Mark is the twelve-time winner of The Times crossword championship and twice Senior World Champion in Sudoku, and Simon is the former record holder for most consecutive correct solutions to The Listener crossword. We hope we can help your puzzle solving while also introducing you to some of the world's best puzzles.

Thank you for watching!
Simon and Mark
▶ Contents ◀
0:00 Theme Music & News around the channel
2:10 Rules of today’s puzzle
5:30 Start Of Solve - Let's Get Cracking!

[SamuPiano]

SamuPiano here! After a month without any split pea puzzles, two in one day?! Such a treat!
Some of the people here may have seen my other comment on Simon's puzzle earlier today, but this was a ruleset I invented in July, which I was originally going to call "split pills." I didn't think that rang very well, though, and I realized that I could theme them nicely if I made them green and shortened the name to "split 'P's", where P stood for pill arrow.
Sorry that the calculations were rather tedious - when I was thinking about it, I added all the hot/cold values at the end; for instance, if a line had 3, 4, 5, and 6 on it and 3 of those were hot, I would think of it as 3+4+5+6 + (3-1) = 20. That reduced a lot of mental math mistakes for me :)
You followed my intended route perfectly through this one, and I appreciate that you gave peas a chance :D

[VonBlade]

Only occasionally do you have a puzzle which is too hard to be remotely enjoyable. It's a grind from start to end. Mark's ability to keep a clear head, a mind for a baffling array of restrictions and the stomach for the task is more impressive here than the recent wrogn one.

[piarittersporn]

It took me a while to solve Simons puzzle, because it confused me at the beginning. Mark's puzzle is more than confusing, it is mind bending. So I gave up after almost two hours. My respect, Mark, for keeping an overview and a clear head.

[johnhantsuk]

Mark has to be commended for getting through that one and only making one mistake.

[AditaBattleForge]

i love the new pea lines! This was a wonderful puzzle! Took me over an hour but it was so worth it, kept me smiling! solve counter 619 in 14 hours!

[patrickgass]

What a fun combination of rulesets! SamuPiano has made something truly special with this one.

[emilywilliams]

Wow. Again, my brain could simply not get going on this ruleset until I had watched over half of your solve, Mark - not because there was any weakness in your explanations, just because it was so strange to me. I think, also, I was still mentally thinking about positive and negative digits (not just +1 or -1). The maths that the constructors of the world make us do, or the mental gyrations necessary to do them, it is all quite bamboozling! Thanks for the video, though, it was very interesting to watch you solve this.

[chocolateboy]

I finished in 106 minutes. This felt a lot harder than than one Simon just did. I really enjoyed this one, though. I quite liked how 111 was an option in this puzzle. I found the break-in to be quite fun as well. I stumbled a bit on the ending, but that was more-so my math ability that gave me pause. Great Puzzle!

[dinane]

For something so complicated and mathy, it is impressive and on brand for this channel that Mark’s mistake was sudoku.

[haxingsheep]

Eloquently elaborated, very interesting puzzle

[Mephistahpheles]

Brilliant puzzle! Challenging rule set to become accustomed. (New rule with hot/cold at the same time was a bit much to manage.)
❤Love the puns, too. <3

Split peas, inner next? Snow peas? Peas of pie? Green peas?

[Xiuhtec]

For some reason I kept getting the +1-1 in my head all mixed up despite usually being quite good at mental math. This one was as a result very tricky for me and it took me over an hour and a half. Got there in the end though and I did enjoy the solve, even if I turned it into a bit of a slog! I like the split pea lines, lots of interesting interplay.

[myfyrmadocjones]

Two peas puzzles in a day, not taking the peas in any way whatsoever. 😀

[MattYDdraig]

47:02
I'd seen a couple of these on the testing channel but not had time to look at them before until now and wow. The concatenation plays havoc enough without the hot/cold yin yang on top. Marvellously done.
I was very glad the box 6/8/9 line turned out the way it did - my first thought after getting my head wrapped around the rules is "wouldn't it be funny if..."

[jimdavis]

How do you treat a hot 9 in a concatenation circle?

[RichSmith]

I must confess, I didn't even consider the possibility of the split-Ps being read in different directions for two lines joining a pair of circles. So it could have been value 01 (blue 1&2) with blue 2 between, or 10 (blue 2&1) with orange 9 between. Another puzzle where I had to pause Mark's solve so I could plug a gap in my own solve.

I think it was most helpful that Simon's puzzle introduced us to split-Ps in a slightly less mind scrambling manner first. This was tough, but very enjoyable.

[stopandthinkpuzzles]

A nice chance to visualize whirled peas.

[Gonzalo_Garcia_]

33:33 for me. Omg what a fantastic solvepath, loved this one!!

[michaurbanski]

Would cold 1 and hot 9 concatenate to 010 = 10?

[RichSmith]

There were moments during Mark's solve where the meaning of "units digit" and "tens digit" seemed to get transposed in his consciousness. (E.g. 34:10, multiple 45:50 - 46:15)