Candice becomes thirsty

Geometry Level 3

Candice, overjoyed at the $100 note she found on the floor earlier, decides to spend it. 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.