A room contains lightbulbs , and switches . Flipping switch will toggle the settings of exactly lightbulbs. All the lightbulbs begin in the off position. For each lightbulb, there is a combination of switches that we can flip which will result in only that lightbulb being on.
We create a table where the entry in row and column is if switch toggles bulb and otherwise. How many different tables can we form?
Details and assumptions
As an explicit example, if switch toggles the settings of lightbulbs to , then the table would be