A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

What day of the week were you born on? Do you know? Here's a way to find out.

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

Choose any 4 whole numbers and take the difference between consecutive numbers, ending with the difference between the first and the last numbers. What happens when you repeat this process over and. . . .

Read this article to find out the mathematical method for working out what day of the week each particular date fell on back as far as 1700.

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

How would you judge a competition to draw a freehand square?

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

A geometry lab crafted in a functional programming language. Ported to Flash from the original java at web.comlab.ox.ac.uk/geomlab

Keep constructing triangles in the incircle of the previous triangle. What happens?

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.