The small breakfast smorg included eggs, bacon, and sausage.
The first diner took one-third of the eggs, one-third of the bacon, and no sausage.
The second diner took one-half of the eggs, no bacon, and one-third of the sausage.
The third diner took one-half of the eggs, two slices of bacon, and two sausages.
The fourth diner took one-half of the eggs, bacon, and sausage.
At that point, one egg, one slice of bacon, and one sausage remained. How much did each diner take, and how much of each item was there originally?
[Fractions refer how much a diner took of what was there at the time.]
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, October 5, 2016 at noon Pacific Time. I will post the answer shortly after.