# Answer to Question #1610 in Integral Calculus for shahriar eftekhari

Question #1610

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

Expert's answer

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⌉

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⌉

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