Cake Cutting

Main cake:

P1 cuts the cake into three pieces they consider of equal size

P2 trims their favourite piece, making it equal to their second

P3 chooses their favourite piece that isn't the trimming

P2 chooses next but has to take the trimmed piece if P3 didn't

P1 takes the remaining piece just leaving the trimming

Trimming:

We call P1 & P2 PA & PB where PA took the trimmed piece

PB cuts the trimming into three piece that they value equally

First, PA chooses their favourite piece of the trimming

Then, P1 chooses their favourite of the remaining pieces

Finally, PB gets the last remaining piece of the trimming

Then we can combine the trim assignments to the main ones