Every Sunday morning, Alice and Beth bake a huge pie together. After it is ready, Alice chooses a positive integer less than 10 and declares it to Beth, then Beth chooses a positive integer less than 10 and declares it to Alice. They slice the pie by making straight cuts with a knife. The number of straight cuts they make is equal to the sum of the two numbers they have chosen. They slice it carefully in order to get the maximum number of slices possible.
After slicing, Alice and Beth take turns eating a few slices of the pie. The number of slices each eats in her turn is never more than 6.
Beth ensures that she gets to eat the last slices on the plate. How does she ensure this?