You and a buddy start with a rectangular cake, represented by rectangle A B C D in Figure 1. Then you get to pick any point E between C and D , and the cake is sliced with two straight cuts, from B to E and E to A . Then it’s your friend’s turn to pick a point F between B and C , so that the cake will be sliced from D to F and F to A . The four straight slices intersect at points G , H , and I as shown in Figure 1. You receive piece A G H I of the cake, and the other player receives pieces D E G , C E H F , and B F I .
Determine all points E you can choose on side C D that will prevent your buddy from ending up with more cake (in all) than you do.