2. Radmila brought a basket of eggs to the market. To the first buyer, she sold half of all the eggs and one more egg. To the second, she sold half of the remaining eggs and one more egg. Similarly, to the third, she sold half of the remaining eggs and one more egg. Then, one egg was left in the basket. How many eggs did Radmila bring to the market?
Solution. First method. Before the third buyer bought half an egg, there were 1.5 eggs in the basket, and before buying half of the eggs, there were 3 eggs in the basket. Before the second buyer bought half an egg, there were 3.5 eggs in the basket, and before buying half of the eggs, there were 7 eggs in the basket. Before the first buyer bought half an egg, there were 7.5 eggs in the basket, and before buying half of the eggs, there were 15 eggs in the basket. Therefore, Radmila brought 15 eggs to the market.

Second method. Let there be $x$ eggs in Radmila's basket. After the first buyer bought half of the total number of eggs and another half egg, there were $x-\frac{x}{2}-\frac{1}{2}=\frac{x-1}{2}$ eggs left in the basket. After the second buyer bought half of the remaining eggs and another half egg, there were $\frac{x-1}{2}-\frac{x-1}{4}-\frac{1}{2}=\frac{x-3}{4}$ eggs left in the basket. After the third buyer bought half of the remaining eggs and another half egg, there were $\frac{x-3}{4}-\frac{x-3}{8}-\frac{1}{2}=\frac{x-7}{8}$ eggs left in the basket. Therefore, $\frac{x-7}{8}=1$, i.e., $x=15$. Finally, Radmila brought 15 eggs to the market.