The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
How can you decide if a graph is traversable?
This problem challenges you to sketch curves with different properties.
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
If you know some points on a line, can you work out other points in between?
A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
Which curve is which, and how would you plan a route to pass between them?
