162. Egg Sales. A woman brought eggs to the market and sold some of them. The next day, her hens worked hard, doubling the remaining eggs, and the owner sold as many as she did the previous day. On the third day, the new remainder was tripled, and the woman sold as many eggs as she did on the previous days. On the fourth day, the new remainder was quadrupled, and on the fifth day, it was quintupled, with the woman selling the same number of eggs each day. By the end of the fifth day, all the eggs were sold.

What is the smallest number of eggs the woman could have brought to the market on the first day, and how many eggs did she sell daily?
162. The smallest possible number of eggs is 103, and the woman sold 60 eggs daily. Any multiples of these numbers can be used as answers to the problem. For example, the woman could have brought 206 eggs and sold 120 daily, or brought 309 eggs and sold 180. Since the smallest number was required, the answer is unique.