Question 52
We have a cube of side $3$ made up of $27$ cubic pieces of side $1$. Inside each piece there is a light bulb that can be on or off. Each time a piece is pressed (it is not possible to press the one at the centre of the cube), the state of its bulb changes, as does the state of the bulbs of the pieces that share a face with the pressed one. Initially, all the bulbs are off. Answer the following questions, justifying your answers:
1. Is it possible to have all the bulbs on?
2. Is it possible to have all the bulbs on except the one at the centre of the cube?
3. Is it possible to have only the bulb at the centre of the cube on?
1. Is it possible to have all the bulbs on?
2. Is it possible to have all the bulbs on except the one at the centre of the cube?
3. Is it possible to have only the bulb at the centre of the cube on?