Follow this recipe for sieving numbers and see what interesting patterns emerge.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?
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?
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
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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.
Given the products of adjacent cells, can you complete this Sudoku?
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. . . .
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Here is a chance to create some Celtic knots and explore the mathematics behind them.