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.

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

How many six digit numbers are there which DO NOT contain a 5?

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.