Pythagoras' Nightmare

*** TODAY'S PUZZLE ***
A debut on the channel today for Matthias J. Raives and a simply wonderful puzzle involving pythagorean triples! At first it'll seem completely intractable but there is a way :)

Do give it a try at the link below:

Rules:
Normal sudoku rules apply. The sum of digits along each edge of a triangle must form a Pythagorean triple, with the largest number of the triple corresponding to the sum along the hypotenuse. There are 12 triangles in this puzzle. Some pythagorean triples include the following (and the multiples thereof): (3,4,5); (5,12,13); (8,15,17); and (7,24,25).

If you manage to solve this one and want more sudoku then give this puzzle from Sam Cavnar-Johnson a try:

It's a classic sudoku with a very cool trick. On Patreon we've released a solve video showing Mark's solve (not knowing the trick) and then Simon's explanation of how to go about it differently :)

For those of you interested in the puzzle Adventure by Jon Schneider (mentioned in the video) there is a video here:

*** PATREON REWARDS JUST OUT ***
Join us on Patreon to participate in the two new competitions! We have two amazing sudoku packs from Panthera, TheAsylum and grkles themed around Japanese Sum Sudoku (which make pictures in the grid if you solve them correctly!).

We've also got Mark's Platinum Jubilee Sudoku and a video on how it was made.

Just $2/month here:

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[gunnervi]

Thanks so much for featuring my puzzle! I came across your miracle sudoku video about a year ago, and have been hooked ever since.

My favorite part about this puzzle is how the little triangles interact with the big one. And its a property I discovered on accident! That's what I love about setting and solving new constraints, you get to work and play with them and by doing so discover how they work.

I'm definitely not done with this constraint, so keep an eye out on the Discord for more like it.

[megatales]

Really like the troll of including the various pythagorean triples to make people (Simon) worry about them, when in the end everything was just a multiple of 3, 4, 5

[DanarkKing]

Simon: explains 'the secret" every episode in case someone doesn't know
Also Simon: everyone knows what a hypotenuse is that watches the channel, I'll skip over it.

[stevieinselby]

Quite entertaining that Simon spends such a long time thinking about the bigger triangles before even looking at the small triangles that are what allow you to get started ... I think that helped a lot of us to beat his time today!

[leemcginty]

I've done one or two puzzles quicker than the video time, but this is the first puzzle that I've completed faster than Simon or Mark. I'm going to ignore the fact that Simon could go faster if he wasn't explaining things so well, but this has given me a feeling of achievement that I couldn't convey to anyone outside this channel! (28:17)

Thanks so much for the great content (both setters and Simon/Mark).

[jshook]

new-to-sudoku undergraduate maths student here; loved this puzzle.

[jessevennard]

I am so grateful for this channel. At first I never imagined I could even break into puzzles of this difficulty. I’m still very amateur but learning more every day thanks to you both. Now… let’s get cracking

[inspiringsand]

Rules: 03:48
Let's Get Cracking: 05:40
Simon's time: 33m26s
Puzzle Solved: 39:06

What about this video's Top Tier Simarkisms?!
The Secret: 2x (21:05, 21:07)

And how about this video's Simarkisms?!
By Sudoku: 8x (26:11, 27:30, 28:58, 29:29, 29:56, 32:23, 33:04, 34:40)
Ah: 7x (15:20, 15:26, 19:23, 20:31, 22:37, 30:31, 35:21)
Clever: 5x (25:12, 26:11, 26:15, 39:09, 39:11)
Nonsense: 4x (17:23, 17:25, 17:33, 17:36)
Hang On: 4x (17:16, 29:35)
Beautiful: 3x (36:11, 36:15, 39:18)
Wow: 3x (09:38, 09:50, 39:07)
Good Grief: 2x (23:04, 29:08)
Sorry: 2x (13:19, 19:32)
Lovely: 2x (26:39, 31:47)
In Fact: 2x (27:52, 34:25)
Obviously: 2x (17:11, 17:23)
Goodness: 1x (24:18)
Bother: 1x (19:23)
Elegant: 1x (06:27)
Gorgeous: 1x (25:59)
Barbaric: 1x (02:47)
Take a Bow: 1x (36:15)
Shouting: 1x (01:58)
Progress: 1x (15:59)
Cake!: 1x (02:02)
Symmetry: 1x (23:50)

Most popular number(>9), digit and colour this video:
Fifteen (25 mentions)
Five (74 mentions)
Red (3 mentions)

Antithesis Battles:
Even (2) - Odd (0)
Higher (2) - Lower (0)
Row (6) - Column (4)

FAQ:
Q1: You missed something!
A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn!
Q2: Can you do this for another channel?
A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!

[lexyeevee]

holy moly, 14:16, probably the biggest margin i've ever beaten simon by. i definitely appreciate these kinds of puzzles where the trick is more about math than about sudoku :)

first i figured out that for a triple (a, b, c) the corner cell must be ½(a + b − c), which made it quickly obvious that tiny triangles only 123/246/369; after that i pencilmarked all the tiny corners, eliminated some 1s, pencilmarked every hypotenuse that could only be 469, and the whole thing swiftly fell apart

[David_K_Booth]

An entertainng puzzle, not too difficult, based on a very novel idea. Thank you Matthias, congratulations on your debut.

[saintender]

Absolutely incredible! As a former math teacher and lifelong math nerd, I was enthralled. Thanks for the set and the solve!

[th.nd.r]

That’s so ridiculously beautiful, that’s one of the best ones in this string of sudoku brilliancies for me. Great setting and solving, and I really want to see this concept/constraint used in future sudokus!

[HunterJE]

Simon wondered at one point about if the hypotenuse of a three-cell triangle spanning boxes to repeat - not only does that not work with the limited digits available, even if you could extend this ruleset to arbitrarily large cell values it would never work because it is impossible to create an integer-sided isosceles right triangle.

[This is related to the irrationality of the square root of 2; if you make a=b and substitute it in to the Pythagorean theorem you get 2a^2 = c^2

Which can be rearranged as such:

2=c^2/a^2
2=(c/a)^2
√2=c/a

If there were a solution where both a and c are integers, the square root of 2 would be rational!]

[Coyotek]

To say this one was in my wheelhouse would be an understatement; at a time of 11:06, this may have been my fastest solve of a non-GAS, 9x9 sudoku at this site. Math *really* played a part in this one.

Fun puzzle!

[emilywilliams]

This was very interesting - and I felt, fairly approachable. I will definitely be making sure that my husband and son both see this one. A lovely and elegant solve, Simon. Thank you!

[johnrupesh]

So simon always explains every basic thing again and again as of toddlers are watching these videos but he doesn't bother explaining the rules this puzzle when it was actually needed. Good job.

[honeyspiderii]

OMG! This is literally the first Sudoku I have ever solved faster than Simon! Yeah, maths! Simon still out-solves me 99 times out of 100 though. Great puzzle, Matthias!

[wokkawicca]

15:48 Found this one easy, probably because I realized right away the small triangles had to be (3, 4, 5) multiples regardless of box-spanning, then went for the fused pair + given digits and left the big triangle for the end.

[BozoTheBear]

I've written so much code for solving puzzles from this channel, especially for generating all killer/sandwich/X-sum/etc combinations. This was definitely a time when the code made things much easier!

[wanderlustwarrior]

31:56 for me. That was a fun puzzle! It went faster after I realized the only digits that could be at the right angle of a triangle with a length of 1 (which incidentally includes the large triangle thanks to overlapping sides) were 1, 2, and 3. But, 1 could never be on certain triangles that see others!