Halving squares

Here is one way to halve a 4 by 4 square into two identical parts along the lines of the grid.

Find five other ways that are different from the one shown and from each other.

Rotations and reflections do not count as “different”.

Tunnel vision

The upper part of a railway tunnel through the Pennines is semi-circular and has a diameter of 10 metres.

What is the maximum height of a train if its wheels are 2 metres from one side?

Halving squares (ages 7 to 12)

SOLUTIONS Tunnel vision (ages 13 to15) This is a simple application of Pythagoras’s theorem, which gives the maximum height of the side of the train as 4 metres