For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

A game that tests your understanding of remainders.

Given the products of diagonally opposite cells - can you complete this Sudoku?

Got It game for an adult and child. How can you play so that you know you will always win?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

A game in which players take it in turns to choose a number. Can you block your opponent?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Given the products of adjacent cells, can you complete this Sudoku?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Can you find any perfect numbers? Read this article to find out more...

Use the interactivities to complete these Venn diagrams.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

If you have only four weights, where could you place them in order to balance this equaliser?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Can you find a way to identify times tables after they have been shifted up?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?