/sci/ - Science & Math

I came up with a random problem.

You have a container, let's say it's one cubic meter and shaped as a cube. You want to fill it with water bottles (the bottles can be any shape you want) such that each bottle is 0.5 liters and they all add up to one cubic meter of water. So there's no empty space in the container. But you want to optimize the container in such a way that the material that has to be used in the water bottles is minimum. The problem is as follows. What is the total amount of material used in the water bottles in terms of surface area?

In other words, how do you divide a cube into 2000 sub-regions each of which have equal volume such that the total surface area of all the subregions is minimized?

A bonus problem is to solve the average surface area of one water bottle if the container is infinite 3D space.

How are younger people performing in maths? Have people looked into that?

Intuition tells me they are not studying enough to unlock their full potential but I don't want to dismiss the possibility of them performing better than older generations, besides nowadays we have access to many resources to study. But are young people even interested in becoming good in mathematics, engineering etc. anymore?

pic unrelated

What is the minimum number of dice throws required such that throwing "n" sixes in a row is more likely to succeed than fail?