## Problem of the week

### 2022-24 Hey, who turned out the lights?

There are light bulbs $$\ell_1,\dots, \ell_n$$ controlled by the switches $$s_1, \dots, s_n$$. The $$i$$th switch flips the status of the $$i$$th light and possibly others as well. If $$s_i$$ flips the status of $$\ell_j$$, then $$s_j$$ flips the status of $$\ell_i$$. All lights are initially off. Prove that it is possible to turn all the lights on.