the executioners had to travel long distances sometimes to get to the place of executions, making them sometimes late,
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Late for what ???
The full moon ???
What ???
Traditionally, the beheadings are carried out in the central square at the end of Friday mid-day prayers. If the town is walled, they would close & lock the gates, so as to create a captive audience.
When my dad worked in Saudi in the 50s, he made the mistake of going into a town for lunch on a Friday, and saw an execution of (IIRC) 3 criminals.
Unlike the Taliban style slow sawing off with a dull knife, it was one fast stroke with a heavy scimitar. Kneeling & bound, the criminal is first lightly poked in the back of the neck, then, as he flinches his head forward, a roundhouse stroke follow to the neck at the base of the skull.