Six years ago, when I took CSP-S 2020, my coding skills were not particularly polished. After finishing the first two problems, I did not have much time left. So when I looked at T4, Snakes, I only wrote a 20-point special-case solution and left in a hurry. Six years later, I learned from Jiang Yanyan's video that many things had changed again in the OI community. This brought me back to Luogu, where I used to practice problems, and I found that after enough attempts, an LLM could even AC a newly released black (i.e. highest difficulty tier) problem that only the problem setter had solved.

Of course, that is not the main point today. The point is that I returned to the T4 Snakes problem where I once scraped together 20 points. A simplified statement is:

There are $n$ snakes, numbered $1,\dots ,n$. Their initial powers are positive integers $a_i$, satisfying

$$a_1\le a_2\le \cdots \le a_n.$$

At any moment, snakes are compared by $(\text{power},\text{index})$: the snake with larger power is stronger; if powers are equal, the snake with larger index is stronger. Therefore the strongest and weakest snakes are uniquely determined.

The current strongest snake may choose whether to eat the current weakest snake. If the strongest snake is $(x,i)$ and the weakest snake is $(y,j)$, then after eating, the weakest snake dies and the strongest snake becomes

$$(x-y,i).$$

Every snake is rational: when it becomes the current strongest snake, it eats the current weakest snake if and only if, under the same rules afterward, it will not eventually die. Otherwise, it refuses to eat, and the game ends immediately. The game also ends when only one snake remains.

The task is to compute how many snakes remain at the end. $n\le {10}^6$.

There are already many solutions to this problem. However, while trying to revisit this problem set, I accidentally came up with another conjecture:

If the initial powers are strictly increasing rather than merely nondecreasing, that is,

$$a_1<a_2<\cdots <a_n,$$

then is the final number of remaining snakes always odd?

The answer is yes, but the proof is much more tedious than I had expected, even more tedious than the idea and implementation of the original problem itself. More importantly, the complete proof was generated entirely by an LLM, which seems to echo the earlier observation about LLMs ACing black problems.

The final workaround is simple: make the same hostname resolve to a VPN/LAN IP during pairing, and to a public IP during public use. Repository: https://github.com/junyu33/moonlight-ios-publicIP

6.16 (d): Challenge Problem. Construct a non-abelian group of order $p^3$ for every prime $p$.

Notation: Let $\lambda$ be the security parameter, and the length of the secret-shared integer be $l$-bits.

Assume having the following basic knowledge in Multi-Party Computation:

• 1-out-of-$k$ ${\text{OT}}_l$ can be implemented using public-key cryptography or similar methods, with a communication cost of $2\lambda +kl$ per instance; using IKNP, this can be reduced to $\lambda +kl$.
• Addition and scalar multiplication based on 2-party additive secret sharing are almost free (no communication overhead).
• Secure multiplication operations for 2-party computation can be implemented using Beaver triples. One secure multiplication operation requires a total communication cost of $2l$.

For floating-point storage, we use IEEE 754 Float32 (single-precision standard):

• $(-1{)}^S\times (1.M)\times 2^{E-bias}$

• Sign bit $S$ 1 bit, exponent $E$ 7 bits, mantissa $M$ 23 bits, $bias=127$

• Round-to-nearest-ties-to-even

Still, I went to the library and borrowed an worn copy of The Myth of Sisyphus. On page two, there was a phone number. I messaged it. Confused, the woman on the other side asked which library. I answered. She said: "I don't remember. It's been too long."

Here's a description of the complete flashing process.

For example, I attempted to edit the firewall settings of the telecom router to block access to the domain names associated with the games.

I'll document the exploration process here, with the correct solution provided in the last section.

This is a heavy topic, but I don't intend to delve into lengthy discussions. Instead, I've chosen a lighter approach: by evaluating the teachers I've encountered from elementary school to university, I hope to sketch a rough outline of education from my perspective.

The original text defines $\tau =2\pi =6.283\cdots$ to replace the current circle constant $\pi$ and lists several reasons for doing so. In addition, I have also included one more reason.

The only dependencies used are the pow function, math.inf, and the deep copy function copy.deepcopy. I also adopted the OOP programming paradigm, which I'm not entirely comfortable with.

Although after writing this, my understanding of both the Weil pairing and OOP has improved (

Given an array of integers nums containing $n+1$ integers where each integer is in the range $[1,n]$ inclusive, $n\le {10}^5$.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array and using only constant extra space.

In the previous article "Building a Fast and Secure VNC Service from Scratch", we achieved a connection from a non-public network machine to a public network machine using DDNS and set up a VNC service on the public machine. In the mid-series article "Learn Intranet Penetration the Hard Way", we used the DDNS-enabled public machine as a jump server to connect to another non-public network machine, thus realizing the dream of working from home. The goal of this follow-up article is to build a web service (specifically Overleaf) on that other non-public network machine based on the mid-series article, allowing local access and ultimately saving the annual $89 subscription fee.