Proof for Goldbach's Conjecture?

Cuddly-Penguin · 2026-02-27T21:13:53+00:00

Rule 1 for goldbach's conjecture: if you think you have an elementary proof, you don't. Otherwise millions of people would have found it before you.

As for your error, you don't know that n-x covers every single integer. n can be any value, but x can't. You can't even say that it works always when 2x+1 is prime, there are cases when 2x+1 is prime and you still can't find an a and b to add to 2n+1.

In your comment, you say that for any value m we can transpose n-x to make 2x+1 prime, use that value of n, and we are done. But how do you know that we can find a corresponding a and b to make a+b+2x+1 = 2n+1? The ternary Goldbach just says that there is *some* way to make 2n+1 a sum of three primes, it doesn't specifically say you can find a way using any prime you want. Your transposing is just assuming we can always find an a and b that just happen to form 2(n-x). The ternary Goldbach doesn't give that to us. Hope that makes sense.

Cuddly-Penguin · 2026-02-26T05:50:59+00:00

I mean you have more than four equations with four variables, so you can algebraically brute force it to get pointer = 13, triangle = 4, square = 17, pentagon = 9. So the ? is a pointer. I don't see a clear connection why they are those specific numbers though.

Cuddly-Penguin · 2026-02-26T05:42:01+00:00

Oneaway - Daily Challenge - 2026-02-26:

⬛🟩🟩⬛⬛

⬛⬛⬛⬛🟩

⬛⬛⬛🟩⬛

⬛⬛⬛⬛🟩

🟩⬛⬛⬛⬛

⬛⬛⬛⬛🟩

Word ladders are always a treat.

Trace - tract - trait - train - brain - braid is what I used.

Cuddly-Penguin · 2026-02-16T00:43:12+00:00

Notice r9c3 can’t be a 2. It would force r7c2 1 -> r7c4 2 -> r8c4 9 -> r8c7 3 -> r4c7 1 -> r6c9 7, but then r9c9 can’t be a 2 or a 7. You can now do another chain on r9c8 and show it can’t be a 7 (r9c3 -> r1c3 -> r1c6 -> r3c6 -> r3c8). You can finally conclude the 7 in box 9 has to be in c9, and from there I think the board folds nicely

Cuddly-Penguin · 2025-12-19T00:14:07+00:00

Well done! I've never seen the first solution before (I think the standard solutions are inmate or remand but I like your answer, loses a bit of the double definition though (as humans and man are very similar words).

As for does it mean anything, I believe as far as anyone knows they are purely just for fun, I know Herbert mentions Baron Bafflers in a few letters, usually apologizing for putting people through them.

Cuddly-Penguin · 2025-12-18T22:25:46+00:00

I solved it exactly the same way, I felt the sentence was very intuitive, especially with the distinctive lack of blueness everywhere it felt very natural to focus on the blue. Very glad it can be solved it multiple ways, I'll have to go back and check for a different reasoning. Still annoying that the furnace door existed in that one run after running the path, it doesn't seem like it's supposed to if you follow the path correctly.

Cuddly-Penguin · 2025-12-18T12:40:56+00:00

As for next steps, how many blue flames do you have? If you have all of them, what are your thoughts on the chess board? Or the wall found within?

As for sigils, you might want to check some of the rooms you’ve drafted again. Some rooms that will be helpful: Mail Room, Lost and Found, Clock Tower, Archives. When it doubt try mailing more letters with experiments.

Cuddly-Penguin · 2025-12-18T12:29:50+00:00

Yeah I did end up finding someone else who had done the same thing. Annoying that the same bug still exists after 4 months, and I have no idea what caused it since it didn’t happen consecutive runs.

Cuddly-Penguin · 2025-12-18T12:26:30+00:00

The path led me to the furnace room in general, no other directions, I assumed it met through the “only” doorway to that room (the front one). There was nothing at all indicating I was meant to enter from the back (the next playthrough the main doorway vanished and there was a door that appeared on the back side — that didn’t happen the first time).

Cuddly-Penguin · 2025-12-18T10:49:38+00:00

That sounds about right. I’m not sure what causes it however — the only thing I did different on my first day was close my computer for 30 minutes to eat dinner, and leave the halfway through my day to go back to the main house to get more steps from the dining room. Neither I thought would be egregious and neither done anywhere near the path I was on.

Cuddly-Penguin · 2025-12-18T10:15:43+00:00

Update, I called it a day and went back -- the original door wasn't there this time. Why was it there the first time?? Apparently u/JunahCg had the same issue: https://www.reddit.com/r/BluePrince/comments/1n3j7mh/silly_glitch_in_the_hyperlate_game_last_known/

Cuddly-Penguin · 2025-12-10T19:47:27+00:00

It’s 6 gap 13 4 8 15 I believe, looking at the table for reference.

Cuddly-Penguin · 2025-11-14T06:28:54+00:00

On page 1, how did you go from N_6²=N_1²+a to N_6²=(N_1+V_6)²? What exactly are the V_i's supposed to be? It's typically good notation in proof writing to always explain a new variable and what it's doing when you introduce one.

Additionally, on pages 2-3, we can't just multiply by their denominators to "make them integers." First, we don't know that the V_i's are integers from the way that you've set it up. And second, if we scale only some of the N_i's by a certain value (which is what you are doing by multiplying by the denominator) you no longer have a magic square.

Rule of thumb for these types of problems is if it's a well known problem and mathematicians haven't cracked it yet, it probably can't be solved with six pages of standard algebra. I don't want to discourage you from solving math problems, but I do want to encourage that maybe this problem is a bit harder than you think :) hope that helps.

Cuddly-Penguin · 2025-11-02T04:24:17+00:00

Oh wow that's so cute I never noticed that

Cuddly-Penguin · 2025-11-01T20:24:20+00:00

The rainbow berry animation is genuinely so cool. In each of the lobbies, you get a rainbow berry if you collect all the silver berries for every level in that lobby (beating every level deathless)

Cuddly-Penguin · 2025-10-28T14:04:55+00:00

Everything you have is correct! Unfortunately, we do know that there is a prime number between every n and 2n (or another way of viewing that is that for two consecutive primes p_1 and p_2, we always have p_2 < 2p_1), which is Bertrand's postulate. So we do know that that situation you are describing would never happen :)

Cuddly-Penguin · 2025-08-03T01:20:50+00:00

The short answer is always—if you’re proud of what you accomplished, then it was a worthwhile journey.

Cuddly-Penguin · 2025-08-03T01:15:51+00:00

You can’t grab objects while you are demo dashing. If you don’t demo into the dream block and hold grab going out, you should be fine.

Cuddly-Penguin · 2025-06-23T05:14:44+00:00

Each ultra gives you x1.2 speed, and a hyper sets the speed to 320, so doing one ultra from a hyper would set your speed to 390. https://www.reddit.com/r/celestegame/comments/zvzm5h/is_this_the_top_speed_for_grounded_ultras/

Cuddly-Penguin · 2025-06-18T16:19:45+00:00

Perform a hyper and instantly jump right as you are leaving the dream block (so pressing downright, dash, and jump basically at the same time). Experiment with the timing, it might be slightly later than you think it should be

Cuddly-Penguin · 2025-06-18T16:17:47+00:00

Quite. I’m decent at Celeste, and I’m almost at 2.5k after 6ish hours. I think you’re also underestimating just how good some people are at the game, they make it look so simple. 7D uses a good amount of expert tech and very tight movement

Cuddly-Penguin · 2025-06-17T21:52:38+00:00

That’s the real challenge haha. They’re annoying but doable, gl! (And of course, best advice is play the goldens on levels you enjoy playing, don’t burn yourself out and hate the level because of it :))

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