The value of each position is the number of times that locker has been "switched" (opened or closed). Imagine that taped to the outside of each locker (or inside, doesn't matter) is a sheet of paper. Every time someone opens or closes the locker, he or she makes a tally-mark on the paper. This way the paper keeps a tally of the number of times the locker has been switched.
In the real world, you can tell if the locker is open or closed just by looking at it, but your model doesn't support that. Instead, how can you tell if a locker is open or closed?