Making any integer with four 2s (2025)

i know everyone plays with their own rules, but from my perspective, a square root spends a 2 - it's not an operator like + or ! . there's an implicit "2" since you could also take the cube root or fourth root

there is a related problem (inspired by an interview questions from ITA software, a part of Google now) that asks to find the smallest positive integer that cannot be expressed using a digit K (in [2,9]) N times in an expression that involves the four basic arithmetic operations and the parentheses: +, -, *, /, (, and ).

to make the problem more interesting, the list of operations can be extended to include exponentiation and concatenation.

for example, using the four basic operations for N=4, and K in [2,9], we get:

7 cannot be computed in 4 2s; 11 cannot be computed in 4 3s; 10 cannot be computed in 4 4s; 8 cannot be computed in 4 5s; 9 cannot be computed in 4 6s; 4 cannot be computed in 4 7s; 5 cannot be computed in 4 8s; 4 cannot be computed in 4 9s;

Popular last year (368 points, 165 comments) https://news.ycombinator.com/item?id=43145753

Spoilsport.

And JFYI since December is near: https://rant.gulbrandsen.priv.no/hack/advent-calendar-for-ne...

Never understood why 7 is considered difficult...

7 = ⌈ 2.2² + 2 ⌉