# If Hannah visits a combined total of four cities in countries X and Y, what is the greatest total number of days she ...

AllieDamron on February 1, 2022

help, how does this make any sense

this last question does not make any sense to me. I cannot get past 6. if hannah has 4 cities she visits between x and y, that would be minimum of 8 days. but we still have to include z. what am i missing/not inferring?

Abigail on February 1, 2022

Hello @alliedamron,

Thank you for your question! This is a tricky one. Hannah spends a total of 14 days in 6 cities with at least 2 days in each city. This gives us two possible distributions of days/cities: either 2-2-2-2-2-4 or 2-2-2-2-3-3 (i.e., she either spends 2 days in 5 cities and 4 days in 1 city OR she spends 2 days in 4 cities and 3 days in 2 cities). To solve this, we will also have to take into account the distribution of cities/countries, of which we have 3 possibilities: 1-1-4, 1-2-3 or 2-2-2.

In this question we are looking to maximize the amount of the days that she could spend visiting cities in country Y, so we’ll take the distribution that allows us to visit the most cities in country Y taking into account that she spends 4 days in total between X and Y. That distribution is 1-2-3 (1 day in X and 3 days in Y for a total of 4 days between the two countries).

The next step is to look to our days/cities distribution to see what the maximum number of cities could be visited in 3 days. If we take the 2-2-2-2-2-4 distribution, we could visit 8 cities in 3 days (2-2-4). So the correct answer is 8.

You asked about Z. In the chosen cities/countries distribution, she would visit 2 cities in country Z, and she would visit them for 2 days each for a total of 4 days in country Z. She would also visit 2 days in country X. So, the total amount of days (2+4+8) equals 14 days. Everything adds up.

I hope this clarifies things. Feel free to follow up if that is still not clear.

Abigail