Making any integer with four 2s (2025)
This delightful mathematical puzzle challenges you to construct any integer using precisely four instances of the digit two. It’s a classic that evolves from elementary arithmetic to advanced functions, captivating HN's technically-minded crowd with its clever solutions. The real kicker? Paul Dirac found a general solution, simplifying everything down to nested square roots, which is both brilliant and a bit of a party pooper for the puzzle enthusiasts.
The Lowdown
The article delves into a classic mathematical puzzle: how to generate any natural number using exactly four instances of the digit 2 and any mathematical operations. This seemingly simple challenge quickly escalates in complexity and elegance as one progresses through different levels of mathematical understanding.
- Initial solutions involve basic arithmetic (addition, subtraction, multiplication, division), accessible to elementary school children.
- As mathematical tools expand to include exponents and factorials, a wider range of numbers becomes achievable.
The Gossip
Recycled Reads
Commenters quickly noted that this intriguing mathematical puzzle is a popular rerun, having graced the Hacker News front page previously. It seems good puzzles, like fine wine, get better with age, or at least warrant a second look.
Seven's Scrutiny
A small but spirited debate emerged regarding the perceived difficulty of generating the number 7. One commenter proposed a solution using a ceiling function and a decimal point, sparking a discussion on the implicit rules of the puzzle, specifically whether decimal points count as valid 'mathematical operations' or merely notation. The consensus leans towards 'no decimals' for purity.