Visualising and representing

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

When Andrew arrives at the end of the walkway, how far is he ahead of Bill?

A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.

What is the minimum number of squares a 13 by 13 square can be dissected into?

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

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?

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?