>>12531166Prove it. Have a problem (people other than OP who know the answer don't interject.

Premise: you have a row of 1000 cubes, numbered 1 to 1000, and a lightbulb, which starts with being switched off. In a move you can pick any two cubes and switch their positions. Every time you do this, the lightbulb changes its state on/off. I.e. the first time you switch two cubes, the light turns on, then if you switch another two cubes, the light turns off again, and so on.

Question: Either:

1. Devise a sequence of switching the cubes so that at the end, the cubes are all back to their starting position, and the lightbulb is on.

2. Prove that this is impossible to do.

If you're actually smart you should be able to solve this.