Making any integer with four 2s (2025)
The gist
Blogger Eli Bendersky explained how physicist Paul Dirac solved the four 2s puzzle for every number.
The debate turns on whether operations like square roots quietly hide extra 2s.
How it unfolded
- 1920sPhysicist Paul Dirac found a general solution to the four 2s puzzle for every number, using nested square roots and base-2 logarithms.
- recentlyEli Bendersky published a post describing the elementary, exponent/factorial, concatenation and Gamma-function approaches and Dirac's general formula.
- recentlyA Hacker News submission of the post by germanrabbit received 6 points and 1 comment; commenter gnabgib noted a prior submission was popular last year with 368 points and 165 comments.
Key terms
- factorials
- The product of all positive integers up to a given non-negative integer, written with an exclamation mark.
- Gamma function
- A mathematical function extending the factorial to complex numbers, defined for all complex numbers except non-positive integers.
- successor function
- A basic mathematical operation that maps a natural number to the next one.
Source: Wikipedia