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.

Image Credit : Wikimedia Marcos Andre
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