MathDB

Let

n

be a fixed positive integer. There are

n \geq 1

lamps in a row, some of them are on and some are off. In a single move, we choose a positive integer

i

(

1 \leq i \leq n

) and switch the state of the first

i

lamps from the left. Determine the smallest number

k

with the property that we can make all of the lamps be switched on using at most

k

moves, no matter what the initial configuration was.
Proposed by Viktor Simjanoski and Nikola Velov

Problem Statement