MathDB

At the beginning of a month a shop has

10

different products for sale, each with equal prices. Every day the price of each product is either doubled or trebled. By the beginning of the following month all the prices have become different. Prove that the ratio (the maximal price) /(the minimal price) is greater than

27

.
(D. Fomin and Stanislav Smirnov, St Petersburg)

Problem Statement