Puzzles

Body Title
hollowed out sphere hollowed out sphere
resistors image 5 Resistors 5
naughts crosses Naughts and Crosses
cylinder of fuel Cylindrical Fuel Tank
liquid in a cylinder liquid in a cylinder
liquid in a cone Liquid in a cone
liquid in a sphere Liquid in a sphere
triangles

This is a simple counting exercise; just make sure you don't miss any!

Triangles
flag colouring 2 Flag Colourings 2
octahedron

What is the volume of a regular octahedron?

Octahedron Volume
resistor matrix 3x3

This is the obvious follow up to resistors-2. In this question, you absolutely must use the Kirchhoff laws.

 

Resistors-3
2x2 resistor matrix

The natural successor to resistors-1. Some interesting strategies and shortcuts start to appear in this problem. We also need to start thinking in terms of Kirchhoffs laws, if not necessary applying them.

 

The first law says that at any given node $$\sum I_k = 0$$

The second law says that around any closed loop, $$\sum V_k =0$$

Resistors-2