Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Given the products of adjacent cells, can you complete this Sudoku?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Here is a chance to create some Celtic knots and explore the mathematics behind them.