Shouldn't it be better if people had to commit suicide in their own houses? I mean if there are 2 people with blue eyes and on the second day they see each othe

Shouldn't it be better if people had to commit suicide in their own houses? I mean if there are 2 people with blue eyes and on the second day they see each other at the town square about to commit seppuko they'd figure perhaps the other is the only one with blue eyes. Or this whole thing went over my head.