Making any integer with four 2s (2025)(eli.thegreenplace.net)
219 points by germanrabbit 4 days ago | 60 comments
tl;dr: A classic math puzzle asks you to express any integer using exactly four 2s and mathematical operations, with difficulty scaling from elementary (basic arithmetic) to advanced (Gamma functions, complex numbers). Paul Dirac "ruined" the puzzle in the 1920s by finding a general solution using nested square roots and base-2 logarithms that works for any integer. His formula technically uses three 2s, but can be padded to four by substituting 2/2 for one digit.
HN Discussion:
  • ↓Challenges the puzzle's rules, arguing square roots or concatenation implicitly use extra numbers and are cheating
  • •Points to alternative or related puzzles and formulations for making integers from limited constants
  • ↑Shares personal nostalgia or enjoyment of similar puzzles from school or holiday traditions
  • ~Suggests simpler solutions exist than the article implies, questioning claimed difficulty levels
  • •Proposes alternative foundational approaches like Peano axioms to trivialize the puzzle