Have you heard of the Liar’s Paradox? 🤥
“This statement is false.”
A simple phrase tries to pass judgment on itself and instantly twists into a logical spiral, denying any stable truth. Language meets its own reflection and falls silent. 🤐

Or the Barber’s Paradox: ✂️
The barber who shaves all those, and only those, who do not shave themselves.
An attempt to define a set by a condition that includes the set itself creates an unsolvable puzzle.
Can a set contain itself as an element? Or… as its defining criterion? 🔄

These loops are a kind of self‑address — an attempt to describe, define, or even generate oneself.
It is a kind of Ouroboros 🐍⭕ — the serpent forever devouring its own tail, an ancient symbol of an endless cycle where beginning and end are indistinguishable, and the system sustains itself while being both cause and effect.

This serpent appears in all aspects of existence, starting in the hazy categories of philosophy ☁️ and ending in the crystalline world of mathematics. ✨
Where the silence of axioms is broken not by a paradox, but by a self‑fulfilling prophecy. 🔮

You will need this🔑
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HINTS
This paradoxes and ouroboros itself are commonly called Self-reference
Sometimes the key is not the number itself, but what it draws.
And the serpent sometimes takes the form of a function

SOLUTION

  1. If you google some bolded words together you will eventually find interesting article or something similar. The easiest way to reach it is self-reference wiki article, then find on page 'mathematic'
  2. Tupper's formula is the formula which plot draws everything you want (even itself) according to some 'k' parameter
  3. Search 'tupper formula online' and find for example this site
  4. Paste the 'k' and you will get TzRxc

Giveaways start on my birthday 🥳 and end on my cakeday 🍰.
Level 1+
No hints and spoilers please. 🙊🚫
Also, check my another train

2 weeks ago*

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very cool fun smart puzzle bump
happy birthday!

2 weeks ago
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View attached image.
2 weeks ago
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Thanks for the train and happy birthday!

2 weeks ago
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Bumping for intrigued but confused!

But also, for happy birthdays!

2 weeks ago
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Bump!

2 weeks ago
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I just made the perfect .gif for when I get stuck on puzzles that are beyond me. Bump :)

View attached image.
2 weeks ago
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Totally lost

2 weeks ago
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Philosophy and maths? I'll leave that one to those who dare.

2 weeks ago
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Philosophy and maths? You'll probably enjoy the book "Gödel, Escher, Bach" by Douglas Hofstadter https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

2 weeks ago
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(っ´Θ`)╮ =͟͟͞͞✨️🎂✨️

Happy Birthday♪

…🔢😊…?
Due to the limitations of the Space translator, the nature of the problem may change, so we will wait and see for a while.

2 weeks ago
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the Truth paradox:
Absolute truth does not exist
All truth is relative

Both statements are self defeating.

But I have no idea what to do with your puzzle.

2 weeks ago
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Do you need to know math to get the aolution?

2 weeks ago
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No, simple Googling is enough.

2 weeks ago
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Why your puzzles are so hard to me lol

2 weeks ago
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Bump! Hints added!

1 week ago
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Fun one for the nerds out here, thanks.

1 week ago
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Hint Bump.

1 week ago
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Tough one, I could not solve it with AI help, we tried 3 hours, but it was fun, have bump!

1 week ago
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2hard4me, but have a bump, belated happy birthday and happy cakeday!

1 week ago
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bump for solved!

1 week ago
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Bump for an extremely unique puzzle!

1 week ago
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Bump for finally solved, interesting approach to a puzzle

1 week ago
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Few hours left bump

6 days ago
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Happy cakeday bump!

This problem is tantalizing with the hints. My brain is mush from crazy busy days plus nights helping my kid with math homework.

6 days ago
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Definitely interested in what the solution is.

Also, happy cakeday.

6 days ago
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Happy 🎂day 🎉

6 days ago
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Would love to see the solution , if you are willing to share, after the giveaway ends.
Happy cakeday!

6 days ago
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