Problems(1)
A set of n lights, numbered 1 to n, are initially off. At every moment, it is possible to perform one of the following operations:
∙ change the state of lamp 1,
∙ change the state of lamp 2, as long as lamp 1 is on,
∙ change the state of lamp k>2, as long as lamp k−1 is on and all lamps 1,...,k−2 are off.
It shows that it is possible, after a certain number of operations, to have only the lamp left on. combinatorics