If a person is changed to it opposite, then the person would have to be "hit" an odd amount of times. The only people who stay like they were in the first place has been "hit" an even amount of times.
So, the only ones who change are square numbers. For instance, If you take a look at the 5th person, the 1st and 5th person make them change. They were hit twice.
If you take a look at a square # such as 9, it will change with the 1st, (changed) 3rd (back to original), and 9th hit.(changed)
If the seat # is a perfect square # ( rational square root), then that seat number will be opposite than it was.
Anonymous wrote in message news://firstname.lastname@example.org... > Hey..please help me with this word problem: > The auditorium at Centennial High Schoool has one thousand seats. > numbered from 1 to 1000, One day each seat was filled and the 1000 > people followed these directions: > > First, each person stood up. > Next, every second person, including the person in seat two sat down. > Then every third person including the person in seat 3, changed to the > opposite. That is, if the person was standing, he or she sat down. If > the person was sitting, he or she stood up. > > Following this, every fourth person, including the person in seat 4, > changed to the opposite. Then, every fifth person, including the > person in seat 5, changed to the opposite, and so on. Finally, the one > thousandth person changed to the opposite. After this last change, was > the one thousandth person sitting or was that person standing? > > Questions: > 1. Was the person in seat 1 sitting or was that person standing? > 2. For which of the seats 1-20 were people sitting? Standing? > 3. Was the person in seat 1000 sitting or was that person standing? > 4. For which of seats 1-1000 were people standing?