"Although the two mice were in different offices the desks were actually effectively back-to-back with a thin plasterboard partition between so kept interfering with each other."
We had a similar jolly in a firm I worked for 10+ years ago. Some bigwig decided that the "clutter free desk" policy meant we should give everyone wireless keyboards and mice. Sadly, the allotted budget to implement this for 130 staff - mixed in with whatever kickback this tie-wearing-jobsworth from the supplier - meant that we ended up with some junk that, instead of "pairing" like most wireless kit - had 4 channels to choose from. Well, you can just imagine the hilarity that ensued.
Luckily - we'd had the foresight to keep the old kit.