Ciro Santilli @cirosantilli 37

This is a summary of the status of the OurBigBook Project, focusing notably on the past 9 months that I've been able to devote fully to it starting June 2024 notably due to the anonymous 1000 Monero donation and other supporters.

I have 3 months left and after unless some crazy person gives more money, I'll go back to some generic programming job that could be done by many other people so that my wife won't kill me. Hopefully I'll find something in quantum computing or AGI research this time that is not too boring, but we'll see.

I should also note that I have raised my requirement for a second year full time from 100k USD to 200k USD, such that there are about only 144k USD missing as of writing, a bargain. See also Section "Sponsor Ciro Santilli's work on OurBigBook.com". I have also set a 2M USD retirement goal in case someone wants to free me to lurk after university students for the rest of my life. Creepy.

The reason for this increase is partly because I'm jealous watching my university peers getting relatively richer and richer than me. More seriously though, as I'm likely going to be looking for a job soon, I don't want to scare employers off too much thinking that it is likely that I'll be leaving in a few months too easily. Plus inflation and the natural lack of security that such endeavour brings.

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GPT-5 by

Ciro Santilli 37 2025-10-27

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Project Euler problem 961 by

Ciro Santilli 37 Created 2025-10-27 Updated 2025-11-05

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projecteuler.net/problem=961

Numerical solution:

166666666689036288

Programs:

euler/961.py

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Andrew He by

Ciro Santilli 37 2025-10-27

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Competitive programmer by

Ciro Santilli 37 2025-10-27

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Updates / Getting banned from Project Euler by

Ciro Santilli 37 Created 2025-10-27 Updated 2025-11-05

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I have been banned from Project Euler for life, and cannot login to my previous account projecteuler.net/profile/cirosantilli.pn

The ban happened within 12 hours of me publishing a solution to Project Euler problem 961 github.com/lucky-bai/projecteuler-solutions/pull/94 which was one-shot by a free GPT-5 account as MathArena had alerted me to being possible: matharena.ai/?comp=euler--euler&task=4&model=GPT-5+%28high%29&run=1

The problem leaderboard contains several people solved the problem within minutes of it being released, so almost certainly with an LLM.

I'm a huge believer in giving answers to problems, and I take the ban with pride.

It is funny to see that people waste their time policing this kind of useless stuff.

Project Euler likely has many fun problems, and can be a useful machine learning benchmark.

The "secret club" mentality is their only blemish, and incompatible with open science.

They should also make sure that LLMs don't one shot their future problems BEFORE publishing them!

Announcements:

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Project Euler problem 943 by

Ciro Santilli 37 Created 2025-10-27 Updated 2025-11-18

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projecteuler.net/problem=943

A naive T in Python is:

from collections import deque

def T(a: int, b: int, N: int) -> int:
    total = a
    q = deque([a] * (a - 1))
    is_a = False
    for i in range(N - 1):
        cur = q.popleft()
        total += cur
        q.extend([a if is_a else b] * cur)
        is_a = not is_a
    return total

assert T(2, 3, 10) == 25
assert T(4, 2, 10**4) == 30004
assert T(5, 8, 10**6) == 6499871

which passes the tests, but takes half a second on PyPy. So clearly it is not going to work for 22332223332233 which has 14 digits.

Maybe if T is optimized enough, then we can just bruteforce over the ~40k possible sum ranges 2 to 223. 1 second would mean 14 hours to do them all, so bruteforce but doable. Otherwise another optimization step may be needed at that level as well: one wonders if multiple sums can be factored out, or if the modularity can of the answer can help in a meaningful way. The first solver was ecnerwala using C/C++ in 1 hour, so there must be another insight missing, unless they have access to a supercomputer.

The first idea that comes to mind to try and optimize T is that this is a dynamic programming, but then the question is what is the recurrence relation.

The sequence appears to be a generalization of the Kolakoski sequence but to numbers other than 1 and 2, also known as the Generalized Kolakoski sequence.

maths-people.anu.edu.au/~brent/pd/Kolakoski-ACCMCC.pdf "A fast algorithm for the Kolakoski sequence" might provide the solution, the paper says:

It is conjectured that the algorithm runs in time $O (n^{α})$ and space $O (n^{α})$ , where $α = l o g (2) / l o g (3) \approx 0.631$

and provides exactly a recurrence relation and a dynamic programming approach.

www.reddit.com/r/dailyprogrammer/comments/8df7sm/20180419_challenge_357_intermediate_kolakoski/ might offer some reference implementations. It references a longer slide by Brent: maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf

www.reddit.com/r/algorithms/comments/8cv3se/kolakoski_sequence/ asks for an implementation but no one gave anything. Dupe question: math.stackexchange.com/questions/2740997/kolakoski-sequence contains an answer with Python and Rust code but just for the original 1,2 case.

github.com/runbobby/Kolakoski has some C++ code but it is not well documented so it's not immediately easy to understand what it actually does. It does appear to consider the m n case however.

Bibligraphy: