Candice becomes thirstyGeometry Level 3
On her way back, she passes by a supermarket and decides to buy herself a beverage. This shop, however, has a very peculiar rule. You can order as many as 20 cans, but will eventually cost a total of $100, irrespective of the number of cans.
Candice picks up \(n\) cans and goes to the cashier. This cashier loves math, and in particular, Geometry, so he tells Candice : "I will provide you a box with a square base such that the side length of the base of this box will be the minimum required to fit all of your cans".
If Candice bought atleast 1 can, how many values of \(n\) are there, such that the cashier provides her with a box of integer side length?
Details and assumptions
- The can is in the shape of a cylinder
- The cans are to be placed in the upright position inside the bag
- The boxes are cuboidal in shape
- The can's base has a radius of 1 unit.