Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located. How many basic states are there?

Since the door that leads to the room is opened, this gives room for particles to move into the next identical room and divided into octants. Now the amount of space that can be occupied becomes double, the number of basic states has increased by 404916