F4LL0UT: The funny thing is that that particular "riddle" doesn't make any sense. Also it's not necessarily an "unwinnable" situation in the classic sense where you just get stuck, IIRC it just inevitably leads to a worse ending.
Well, it did make sense for me, at least at the time. You are told not to do that "thing" literally minutes before when "coming up with a plan". I only found out the "unwinnable" situation because, after beating the game, I wanted to see what happened "going alone", so to speak (and also trying all the combinations with the costumes and such). And if I don't remember this wrong, you ended up with the "I really don't want to be dead" screen, right? Only that if you didn't have a savegame from before that part... you'll die again and again, no other option. But you are right: you can continue playing.
Just wanted to warn the OP, so he/she didn't need to play all the game again in case something goes wrong. GK1 is the only in the series when you need a savegame if you die: there is no going back otherwise (the options are "restore" and "restart"). Thankfully, they fixed that in GK2.
And, hopefully, this won't be a problem in the remake.