Thierry, Hugo, and Caroline want to share their favourite chocolate cake.
How to process to satisfy that each of them (i.e. no one would swap his/her piece against another one) ?

Note : with only Thierry and Hugo, a method is : Thierry cuts the cake into two pieces he thinks to be equally large. Whatever piece he will have, he'll be envy-free because he believes both portions are equal. Hugo chooses one of the two pieces, and is also happy because he can get the piece he prefers. (If one writes T and H for the pieces going respectively to Thierry and Hugo, Thierry's measure of each piece is µ_T(T)=µ_T(H)=1/2, while for Hugo µ_H(H)≥1/2≥µ_H(T)). The question is : how to do if Caroline joins them?


Hmmm, good brownies