Official Dyalog APL 2016 Year Game
Hexagony, 888 bytes

Okay, first some ground rules for Hexagony, in case anyone wants to beat this:


I'm interpreting "snippet" as a linear piece of code that can be dumped into any sufficiently large program, provided the current and adjacent memory edges are zero.
The snippet has to be entered from the left and exited from the right. I'd be able to save quite a bunch of bytes without that (e.g. 2|016 for 22), but it seems most in the spirit of the challenge.
The snippet "produces" a given number, if any memory edge (not necessarily the current one) holds that value after execution.
The rule forbidding any other numbers in the snippet affects both other digits as well as any letters, since they effectively act as integer literals in Hexagony. (Those would save a ton of bytes.)


So here is the list. I did test most of them but not all (some are trivial modifications of others), so I hope I didn't make any mistakes:

2016
20&amp;1}6
2}016
2)}016
20{16'-
201}6(
201}6
201}6)
2}016":
2(0(}16
2(0}16
2(0)}16
)2}016
)2)}016
20}16((
20}16(
20}16
20}16)
20}16))
20(}16
20}16
20)}16
20))}16
20)))}16
20}1)6((
20}1)6(
20}1)6
20}1)6)
201{6)':
2)0(}16
2)0}16
2)0)}16
2{016'*
201{6':
2{016)'*
20}1))6(
20}1))6
20}1))6)
20}1))6))
2))0(}16
2))0}16
2))0)}16
2))0))}16
2))0)))}16
20)){1)'6*
2){016('*
2){016('*)
2){016'*(
2){016'*
2){016'*)
2)))0}16
2){016)'*
2){016)'*)
2{01)6)'*(
2{01)6)'*
2{01)6)'*)
2{01)6)'*))
2{01)6)'*)))
2))))0((}16
2))))0(}16
2))))0}16
2))))0)}16
2)0){1)'6*
2)){016'*(
2)){016'*
2)){016'*)
2)){016'*))
2)){016'*)))
2{01))6('*(
2{01))6('*
2{01))6'*((
2{01))6'*(
2{01))6'*
2{01))6'*)
2{01))6)'*
2){01)6('*
2){01)6'*((
2){01)6'*(
2){01)6'*
2){01)6'*)
20{1)))'6*
2){01)6)'*
2){01)6)'*)
2){01)6)'*))
2){01)6))'*
2){01)6))'*)
2){01)6))'*))
2){01)6)))'*
2{01)))6(('*
2{01)))6('*(
2{01)))6('*
2{01)))6'*(
2{01)))6'*
2{01)))6'*)
2{01)))6)'*
2{01)))6)'*)
2{01)))6))'*
2(01((((}16
2(01(((}16
2(01((}16
2(01(}16


I got a bit lazy towards the end, so I'm sure this isn't optimal. Might be interesting (and possible) to brute force these.