If Friday rolls around the prisoner knows he is going to be executed right? Why can’t the execution be held the next week on Monday through Friday, which gives an endless possibility of days to execute the prisoner, seemingly making it impossible for him to know which day he will be executed on. Or was this condition already ruled out?
I know a simple way to solve it. It never states that the man has a cell with a window, a calander or clock. If he is in a windowless room with no clock or calander, and cannot judge the time of day to schedule a normal sleep routine. He will never know what day or time it is, and can never know if it is friday or not. You can kill him at you convience. Just have a cell with a thousand holes in the upper walls and shoot him (probably in the back as he will never realize it until the shot).
actually, the man dies of natural causes on Monday.