One that has perplexed me badly is what I refer to as The Box Theorem. This involves a cat in a box. If I take this cat in a box, and put the whole thing in another, larger box, then will the boxes cave in on themselves and all that will remain is the cat, sitting on the floor where the boxes once sat.
I tried it with my dog and it didn't work, but I still think it's possible. Something to do with cat DNA no doubt.
Another mathematics problem I'm having involves calculating the distance between me and a guy wearing a headband at any given point in time. Struggling with that.