How quickly can a legal game reach a position where one side must give checkmate?
This is in effect Evergalo's reading (see his (now deleted) answer) of Rewan Demontay's Question 33154; that question actually asked something else, but the selfmate question is nice too. Evergalo offered a game that reaches such a position in 6.0 moves, i.e. after Black's 6th:
[FEN ""] 1. e3 d6 2. Ke2 Qd7 3. Kd3 Qh3 4. Qh5 Kd7 5. Ke4 Ke6 6. d4 Qf5+ 7. Qxf5#
I found a solution in 5.5, that is, after White's 6th move (actually two very similar positions, which together can be reached in 660 ways according to Popeye 3.41).
Is 5.5 moves the quickest possible?
If so, are there other solutions in 5.5 ?
Has this puzzle appeared before?