MMXVI

The idea is to only use the year’s digits — preferably in order — and mathematical symbols (+, -, \cdot , \sqrt{}, \lfloor\rfloor, \lceil\rceil, \dots) to create an equation that evaluates to a specific day of the month.
The 0th of December, 2016 would, for example, be 2 \cdot 0 \cdot 1 \cdot 6, 2^0 - 1^6 or \lfloor \frac{2}{0 + 16} \rfloor.

1 = 2 \cdot 0+1^6
2 = \sqrt{20-16}
3 = (2+0)^{-1} \cdot 6
4 = 2^{0+ \sqrt{\sqrt{16}}}
5 = 2 \cdot 0-1+6
6 = 2 \cdot 0 \cdot 1+6
7 = 2 \cdot 0+1+6
8 = 2+0+ \sqrt[1]{6}
9 = 2+0+1+6
10 = 2+0!+1+6
11 = -\lceil \sqrt{20} \rceil+16
12 = 2 \cdot (0!-1+6)
13 = -(2+0!)+16
14 = -(2+0)+16
15 = -(2 \cdot 0)!+16
16 = 2 \cdot 0+16
17 = 2^0+16
18 = 2+0+16
19 = 2+0!+16
20 = \lceil \sqrt{20} \rceil \cdot \sqrt{16}
21 = 20+ \lfloor \sqrt{\sqrt{\sqrt{16}}} \rfloor
22 = (2+0!)!+16
23 = (2+0!+1)!- \lfloor \sqrt{\sqrt{6}} \rfloor
24 = 20+ \sqrt{16}
25 = 20-1+6
26 = 20+1 \cdot 6
27 = 20+1+6
28 = 2+0-1+ \lceil \sqrt{6!} \rceil
29 = 20+ \lceil \sqrt{\lceil \sqrt{(1+6)!} \rceil} \rceil
30 = (2+0!+1)!+6
31 = \lceil \sqrt{\sqrt{\sqrt{\sqrt{20!}}}} \rceil +16

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