[sinkwool]

Can you explain more? (I might be stupid and don't see some obvious proof of why your approach is correct), but intuitively it doesn't seem that the fact that the cup is symmetrical is enough. Say if the handle of the cup was really really big, while still preserving symmetry, then its outstanding area would be huge compared to what the doughnut could cover.

[latexr]

> Can you explain more?

https://i.imgur.com/yE43nun.png

https://i.imgur.com/NTfbt5U.png

Note how the middle of the donut aligns with the bottom or top of the cup.

> don't see some obvious proof of why your approach is correct

I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.

[sinkwool]

Thanks for the reply and for the screenshots. before writing my initial reply, I went back and tried to get a 50/50 split based on your comment and came up with the same solution. But I didn't understand why it worked. I now believe it's either pure luck, or there's something about the sizes that result in a 50/50 split.

I think it's easy to see that if the central hole of the doughnut were either smaller or larger, or if the handle of the cup was smaller or larger, these splits would not work.

> I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.

Sure, that's fair, it's just that your original explanation for how the solution is to swap the problem from splitting the cup to splitting the doughnut was so intriguing and puzzling that got me curious.