Problem installing libinput on 16.04.2

Solution 1:

So I submitted a bug report and the response was this:

You're not supposed to have xserver-xorg-input-libinput installable, that's not possible 
because it's bound to the server input ABI

install xserver-xorg-input-libinput-hwe-16.04 instead

Installing the renamed package worked. These appear to have been recently renamed which is where the confusion is coming from.