Coordinates

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

What is the area of the triangle formed by these three lines?

Find the shape and symmetries of the two pieces of this cut cube.

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?