In the version where one prisoner is taken in per day, the solution can be drastically simplified if it is agreed that the prisoner who is taken into the first day is the counter.
That case only requires flipping switch a off 22 times after the first day.
Obviously, removing that single bit of information makes the solution much harder to find, but adding then later removing it makes discovering the solution a more iterative thing. Which is desirable if, for example, you're giving these puzzles to your kids.
I think you missed the part where he said "In the version where one prisoner is taken in per day", in which case it _is_ possible to know if you are the first to go into the switch room.
That case only requires flipping switch a off 22 times after the first day.
Obviously, removing that single bit of information makes the solution much harder to find, but adding then later removing it makes discovering the solution a more iterative thing. Which is desirable if, for example, you're giving these puzzles to your kids.