mathematics - No broken eggs puzzle

Three men went to buy eggs from an eggs seller:

1. The first ordered half of the seller's stock plus half of an egg.


2. The second ordered half of what's left in the stock plus half of an egg.


3. The third ordered half of what's left in the stock plus half of an egg.

How many eggs did the seller have in his stock knowing that:

1. No eggs were broken in the process.



2. The seller's stock is now empty (no eggs left).

Answer

This can be easily solved starting from the third guy since no egg is left after he took the half of the egg.

Third guy:

Half of the egg has to be equal to half of the stock, because he took first half of the stock then the rest (which is half of an egg), resulting third guy got $1$ egg only.

Second guy:

When second guy bought whatever he says, there are 1 egg left. We know this from above. So $1$ egg+$\tfrac{1}{2}$ egg has to be equal to the half of the stock. So there were $3$ in the stock when second guy decided to buy some eggs, meaning he got $2$ eggs.

First guy:

With the same logic, after the first guy bought the eggs, there are $3$ eggs left. meaning $3$ and and a half should be the other half of the egg, resulting $7$ was the total number of eggs at the very beginning and first guy bought $4$ eggs actually.