Farkas: If r18-p19-s18-s19 instead of r18-p19-s18-t18, then Black doesn't have a better answer than ko.
Which means for White t18 is a stronger move then s19.
The same goes for s17, that is what KoichiX meant.
This means this problem is not correct, because you must assume, that White always chooses the strongest and best moves. (Noone would choose an unconditional death instead of ko.)
d4rkm4tter: I see. I added the sequence r18-p19-s18-s19.
If r18-p19-s18-s19 instead of r18-p19-s18-t18, then Black doesn't have a better answer than ko. Which means for White t18 is a stronger move then s19. The same goes for s17, that is what KoichiX meant. This means this problem is not correct, because you must assume, that White always chooses the strongest and best moves. (Noone would choose an unconditional death instead of ko.)