A blog post challenges readers to solve a math puzzle involving predicting the output of a hypothetical AI model trained on specific numerical sequences. The AI, named "Predictor," is trained on sequences like 1,2,3,4,5 -> 6 and 2,4,6,8,10 -> 12, seemingly learning to extrapolate the next number in simple arithmetic progressions. However, when given the sequence 1,3,5,7,9, the AI outputs 10 instead of the expected 11. The puzzle asks readers to determine the underlying logic of the AI and predict its output for the sequence 1,2,3,5,8. A symbolic prize (bragging rights) is offered to anyone who can crack the code.
The post explores the mathematical puzzle of representing any integer using four twos and a limited set of operations. It demonstrates how combining operations like addition, subtraction, multiplication, division, square roots, factorials, decimal points, and concatenation, along with concepts like double factorials and the gamma function (a generalization of the factorial), allows for creative expression of numerous integers. While acknowledging the potential for more complex representations using less common operations, the post focuses on showcasing the flexibility and surprising reach of this mathematical exercise using a relatively small toolkit of functions. It ultimately highlights the challenge and ingenuity involved in manipulating a limited set of numbers to achieve a wide range of results.
Hacker News users generally enjoyed the puzzle presented in the linked article about constructing integers using four twos. Several commenters explored alternative solutions using different mathematical operations like bitwise XOR, square roots, and logarithms, showcasing a playful engagement with the challenge. Some discussed the arbitrary nature of the "four twos" constraint, suggesting that similar puzzles could be devised with other numbers or constraints. A few comments delved into the role of such puzzles in education, highlighting their value in encouraging creative problem-solving. One commenter pointed out the similarity to the "four fours" puzzle, referencing a website dedicated to exploring its variations.
"Subway Poker" is a silent, observational game played by mentally assigning poker hands to fellow subway passengers based on the first five visible digits of their MetroCards. Players cannot influence the cards they are "dealt" and simply observe the hands around them, comparing their imagined hands to others' to determine a winner. The game offers a discreet and engaging way to pass the time during a commute, adding a layer of amusement to the mundane act of people-watching.
Commenters on Hacker News largely enjoyed the subway poker concept, calling it "charming" and "delightful." Some discussed strategies, like focusing on suits rather than specific card values for easier memorization, or intentionally losing rounds to mislead other players. A few debated the feasibility of the game in real-world scenarios, citing crowded subways and the difficulty of maintaining eye contact. Several expressed interest in trying it themselves, while others suggested variations, like using phone apps or playing with larger groups. Some reminisced about similar silent games played in childhood. The overall sentiment was positive, with the game seen as a fun and engaging way to pass the time on public transit.
Summary of Comments ( 9 )
https://news.ycombinator.com/item?id=43538986
HN users generally found the AI/Math puzzle unimpressive and easily solvable. Several commenters quickly pointed out the solution involves recognizing the pattern as powers of 2, leading to the answer 2^32. Some criticized the framing as an "AI" puzzle, arguing it's a straightforward math problem solvable with basic pattern recognition. Others debated the value of the $100 prize and whether it justified the effort. A few users noted potential ambiguity in the problem's wording, but these concerns were largely dismissed by others who found the intended pattern clear. There was some discussion about the puzzle's suitability for testing AI, with skepticism expressed about its ability to distinguish genuine intelligence.
The Hacker News post titled "AI/Math Puzzle" linking to an article about an unsolved math problem related to AI generated text has a moderate number of comments, sparking a discussion around the puzzle's difficulty, potential approaches, and the nature of the challenge itself.
Several commenters discuss the ambiguity of the problem, particularly focusing on the interpretation of "random" and its implications for solving the puzzle. One commenter suggests the problem is ill-defined because the concept of "random text generated by a large language model" lacks a precise mathematical definition. They argue that without specifying the underlying distribution of the LLM's output, the problem becomes intractable. This point is echoed by other users who highlight that the inherent complexity and evolving nature of LLMs make it challenging to establish a fixed probabilistic framework for analysis.
Another thread of discussion revolves around the computational feasibility of brute-force approaches. Some commenters suggest that the vast search space makes it impractical to solve the puzzle by simply enumerating all possible strings and checking if they satisfy the given conditions. One user proposes a more targeted approach by focusing on shorter strings, arguing that the probability of finding a solution increases with decreasing string length.
A few commenters also touch upon the philosophical implications of the puzzle, pondering the nature of randomness and its relationship to AI-generated text. One user raises the question of whether LLM output can be considered truly random, given its deterministic nature. Another commenter speculates about the potential connection between this problem and other areas of mathematics, such as Kolmogorov complexity.
Finally, some comments express skepticism about the puzzle's originality and significance. One commenter questions whether the problem is genuinely novel or simply a repackaged version of existing mathematical concepts. Another expresses doubt about the practical value of solving the puzzle, suggesting that it may be more of a recreational challenge than a significant scientific endeavor. Despite some negativity, several users express interest in the problem and share ideas for potential solutions, demonstrating the engaging nature of the puzzle.