Is it possible to sequentially generate all $n$-bit configurations (say, the binary representation of a an $n$-digit number), a single bit flip a time, in such a way that no configuration is generated twice?
If yes, is there an algorithm for this that doesn't need to remember which configurations have already been generated?
Example for 3-bit configurations
OOO OOX OXX OXO XXO XOO XOX XXX
Subsequent configurations differ only in a single bit.