Problem number 22. Zara wants to move through the grid from A to B. She can only move to the right or upwards. Each time she visits a gray box, she has to pay one dollar. Each time she visits a white box, she has to pay two dollars. How much would she pay for the cheapest path? Eleven dollars? Twelve dollars? Thirteen dollars? Fifteen dollars? Or sixteen dollars? Zara pays more for going through a white box than a gray box, so we need a path of as few white boxes as possible. Since she can only move up or to the right, the total path length will be eight. This problem is best solved by guess and check. If we go through the middle of the column, we can go through three gray boxes and five white boxes. We can try different paths, but we will never find a path with fewer white boxes. Now let's find the cost. The cost will be two dollars for each white box and one dollar for each gray box. So it will be two plus two plus one plus one plus two plus one plus two plus two or thirteen dollars. So the answer is C, thirteen dollars.

grid traversal

minimum cost path

gray boxes

white boxes

Zara's journey