premise: Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city. If Hannah visits an equal number of cities in each of the countries, what is the greatest total number of days she can spend visiting cities in country X?
hypothesis: 4