Answer to Question #1610 in Integral Calculus for shahriar eftekhari

Question

how can we make numbers from 1 to 15 with three 2? (you can make this numbers only with+,-,*,/,√,⌊…⌋,⌈…⌉,...^...) e. g. :6=2+2+2 3=(2+2)-⌊2√⌋ please answer me only if you can make all of the numbers

Answer 1

1 = ⌊√2⌋+⌊√2⌋-⌊√2⌋
2 = 2+2-2,
3 = 2+2/2,
4 = ⌊√2⌋+⌊√2⌋+2
5 = 2^2 + ⌊√2⌋
6 = 2+2+2
7= ⌈√22⌉+2
8 = (2+2)*2
9 = (2 +⌊√2⌋)^2
10 = ⌈√22⌉*2
11 = 22/2
12 = ⌈(√2+2)^2⌉
13 = log2(log2(√√√√√√√√√√√√√2))
14 = ⌊√222⌋
15 = ⌈√222⌉