An egg salesman was asked how many eggs he had sold that day.
He replied, "My first customer said, 'I'll buy half your eggs and half an egg more'. My second and third customers said the same thing.
When I had filled all three orders, I sold out of eggs without having to break a single egg the whole day."
How many eggs were sold in all?
Let the total number of eggs sold be x.
The first customer bought (x/2 + 1/2) eggs, leaving behind
x - (x/2 + 1/2) = (x/2 - 1/2) eggs.
The second customer bought 1/2(x/2 - 1/2) + 1/2 = x/4 + 1/4 eggs, leaving behind (x/2 - 1/2) - (x/4 + 1/4) = x/4 - 3/4 eggs.
The third customer bought 1/2(x/4 - 3/4) + 1/2 = x/8 + 1/8 eggs, leaving behind (x/4 - 3/4) - (x/8 + 1/8) = x/8 - 7/8 eggs.
However, by the problem, the third customer did not leave behind any egg.
Accordingly, we must have:
x/8 - 7/8 = 0, giving: x = 7
Consequently, the required number of eggs is 7.