Millennium’s 2024 Brainteaser: Decoding the 3^2025 Puzzle
Today, we present a brain teaser from Millennium Management.
Millennium is a global leading hedge fund manager, founded in 1989 by Israel Englander, an Israeli-American financier. As of June this year, its assets under management (AUM) stood at $67.7 billion, with over 5,500 employees. By 2022, the net returns of its managed products ranked fourth among hedge funds established after 1989.
Internally, Millennium operates on a "horse racing" mechanism, currently comprising approximately 330 investment teams. Individual investment styles are not restricted; performance is the sole metric, creating a competitive environment.
The firm provides a robust platform for its investment teams. Currently, it manages over 2,000 datasets from 400 suppliers, totaling 10 trillion data records and over 2,000 TB of compressed storage.
The puzzle is as follows:
In simple terms, the number $N$ consists of $3^{2024}$ digits of '3'. The task is to identify the largest power of 3 that divides $N$. If we scale down the problem, $N=333$ or $N=333,333,333$ are valid inputs, whereas $3,333$ or $33,333$ are not. The optimal answers in these smaller cases are 9 and 27, respectively.
Millennium typically releases the answer alongside the puzzle, enhancing its entertainment value. This contrasts with Jane Street, which does not immediately release answers. At Jane Street, submitting an answer may earn you a spot on the leaderboard, reflecting a talent-selection approach.
The answer provided by Millennium is $3^{2025}$. Did you solve it?
This problem is roughly at the level of middle school math olympiads. Providing the answer is straightforward, but it tests logical reasoning, mathematical foundation, and creative problem-solving skills.
Although Millennium’s brain teasers are not directly linked to talent screening, solving them is beneficial. Why?
If you are applying to a company, you should thoroughly research it. If you are interviewing for a sales role, you should know their products, clients, and competitors. If you are interviewing for a technical role, you should understand their tech stack and depth. At the very least, you should determine whether you would enjoy working there, beyond just the salary.
If you are unwilling to engage with their website’s brain teasers, how can you claim to love the company?
Regarding career development, let’s return to Millennium’s horse racing mechanism. While this structure offers opportunities, it also creates pressure, leading to employee turnover, particularly among strategy developers who may not stay long-term.
However, experience at Millennium serves as a golden ladder, significantly benefiting future career prospects.
Abroad, many individuals at WorldQuant come from Millennium (partly due to a joint venture established in 2018).
In China, core figures at top private equity funds often have Millennium backgrounds, such as Wang Chen and Yao Qicong at Jiukun, He Wenqi and Zhang Wancheng at Chengqi, Qiu Huiming at Minglong, and Ma Zhiyu at Lingjun.
Let me ask one last time: Did you solve this puzzle? If you are familiar with Python 3.8’s new syntax for number representation, which allows underscores in numeric literals (e.g., 333_333 for 333,333), wouldn’t it be easy to guess the answer and understand the underlying principle?
333
333_333_333
333_333_333_333_333_333_333_333_333