This is a really hard for me to remember the specific episode/chapter... and even though the person did NOT die (was saved by Conan) It is a brutal way of killing someone. I'll just explain the method:
There was like a rope tied to a big cinderblock(.. a rock, for people who don't speak english

) and the rope was also tied around a big block of ice and I GOT IT!.. hold on I'm pretty sure I remember the ep.
K.. no. I didn't. K so anyway the rope is also tied around the ice which makes it suspended in the air and the victim's head is laid directly beneath the drop point of the cinderblock. Eventually the ice melts and the rope breaks and the block falls, but Conan had just saved the guy.. I feel like it was a recently DCTP-released ep.. but I'm not sure. It involved a man who was acting very strange and he OHHH! I got it! 276! The Missing Policeman's Notebook! But yeah, thats a brutal way to
attempt killing someone.