Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

When is 7^n + 3^n a multiple of 10? Use Excel to investigate, and try to explain what you find out.

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.