TsumegoFromGames173/Attempts

Black's liberties  

(s/shared o/outside a/approach e/eye)

The points are neutral. Black's cutting stones actually don't have more liberties than the whole group because in this case Black would have to play the last/only approach liberty (no eye anymore), and he would have one less approach liberty as White could fill from the right side (formerly eye side). Black should connect in all cases.

White's outside liberties  

Incidentally, even if black had 2 liberties fewer, he could still win because the throw-in removes one liberty from white.

For the same reason, Black could throw-in in the original problem to remove the 6 ko-threats remaining in the area.

Dieter: Agree. I must admit that when approach moves and cutting points are part of the problem, I prefer to read it out instead of adjusting the heuristics.