Coordinates

problem
Corridors

Age

14 to 16

Challenge level

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

Age

14 to 18

Challenge level

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?
problem
What are you plotting?

Age

7 to 11

Challenge level

Investigate the positions of points which have particular x and y coordinates. What do you notice?
problem
Treasure island

Age

7 to 11

Challenge level

Write down what you can see at the coordinates of the treasure island map. The words can be used in a special way to find the buried treasure. Can you work out where it is?
problem
Transformation tease

Age

7 to 11

Challenge level

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?
problem
A Cartesian puzzle

Age

7 to 11

Challenge level

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
problem
A tilted square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Square pair circles

Age

16 to 18

Challenge level

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.
problem
Parabella

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.
problem
Hypotenuse lattice points

Age

14 to 16

Challenge level

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?