So Jeremy cuts the first cake in the ratio 3:1, and no matter which portion Marie picks, she’ll end up with 3/4 of a cake (neglecting crumbs).

If Jeremy cuts a smaller piece than 1/4 from the first cake, Marie chooses the bigger portion and gets more than 3/4, so he’s not going to do that.

If Jeremy cuts a bigger piece than 1/4 (up to 1/2), Marie will take the smaller (but >1/4) plus half of the second cake, so she’ll end up with >3/4.

So: 1 1/4 cake for Jeremy–assuming Marie consents to the entire arrangement.

]]>