Question 17
There are $2n-1$ light bulbs in a row. Initially the middle ($n$-th) bulb is on and all the others are off. In one step it is allowed to choose two non-adjacent bulbs that are off, such that all bulbs between them are on, and to change the state of these two bulbs and of all bulbs between them (for example, from the configuration $\bullet\circ\circ\circ\bullet$ one obtains $\circ\bullet\bullet\bullet\circ$, where $\circ$ denotes a bulb that is on and $\bullet$ a bulb that is off). What is the largest number of steps that can be performed?
(Dušan Đukić)
(Dušan Đukić)