u/WeCanDoItGuys

For some notational consistency:
Use the shortcut odd step: T(x) = {x/2, even; (3x+1)/2, odd}

Let the number of steps be n, and the number of odd steps be m.
If x follows a given parity sequence (example: EOEOOEE), then

• kᵢ are the indices of the odd steps (example: [1,3,4]), and
• S = ∑2^(kᵢ)3^(m-1-i) from i=0 to m-1 (example: 2^(1)3^(2) + 2^(3)3^(1) + 2^(4)3^(0))
• So, T^(n)(x) = (3^(m)x + S)/2^(n)

Per a proof in a stackexchange answer, the title claim is true, but can you prove it?

"Hulk Smash!" is two words that represent the destructive capabilities of man to waste any excess food. Thanos chose between a crisis or abundance. In a crisis, humanity would look into themselves, and after some time, reform. But in abundance, humanity would look outward at the new resources and destroy them at double the pace. Thanos sees this not just as a human thing, but a universal, greedy, growing amorphous thing present in all intelligent life. An uncontrollable monster inside of us all, the Hulk of it all that sees unsmashed things and mindlessly smashes them.

According to wikipedia and some youtube videos, these problems can be reduced into each other:
- 3SAT, Graph Coloring, Clique
- Knapsack, Traveling Salesman, Exam Scheduling
- Minesweeper, Tetris, Sudoku, Gem Swap

It would be really neat to be able to write out a boolean satisfiability problem and then an online tool shows you the minesweeper board or knapsack item values or whatever that correspond to that problem. Does anything like that exist?

I wrote a whole thing explaining this but sadly my computer crashed and the draft was lost.

In short, x's parity sequence is its odd (1) and even (0) steps it follows. Below is my python code for putting in a parity sequence (like [1,1,0,1,0,0,1,1,1,1]) to view which initial number would follow it. Try it here!

from itertools import compress

parity_seq = [1,1,0,1,0,0,1,1,1,1]
m = parity_seq.count(1)
n = len(parity_seq)

def S_ki(parity_seq):
    ki = compress(range(n), parity_seq) #https://stackoverflow.com/a/71101281
    return sum(((2**one_index)*(3**(m-1-i)) for i,one_index in enumerate(ki)))

def x0_from_parseq(parity_seq):
    return (-pow(3,-m, 1<<n)*S_ki(parity_seq)) & ((1<<n)-1) #(x & ((1<<n)-1)) instead of x%(2**n)

print(f"2^{n}t + {x0_from_parseq(parity_seq)}")

If God is good, why are those who do not follow Him tortured for eternity? "That is a natural consequence of being apart from Him after death." But God writes reality, why should He be unable to change such a law?

---

Humanity is faced with two choices.

• Protest the existence of Hell. Refuse to follow God, so that He abolishes Hell.
• Follow God.

If enough people protest God (percentage unknown), He may abolish Hell.
If you follow God, you will go to Heaven no matter the outcome of the protest.

What choice do you make?

https://preview.redd.it/h4idg03d9bch1.png?width=2557&format=png&auto=webp&s=e10395686408ab7735964c205c861634161ebf42

https://youtu.be/CGPp1XIScsA?t=88

These peeps have superpowered brains and manipulate events from the background to achieve their end goals.

Round 1: If each of them was a campaign manager for a particular candidate, whose candidate would win?

Round 2: If each of them were trying to kill the other two, who would win? They're not on a battlefield, they're just in civilization, and they can take as long as they like.

Round 3: If they each devised a game for all three of them to play, who if any would win two out of three games?