Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Can you explain the strategy for winning this game with any target?

Find out about Magic Squares in this article written for students. Why are they magic?!

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

This dice train has been made using specific rules. How many different trains can you make?

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

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

You have 5 darts and your target score is 44. How many different ways could you score 44?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Here is a chance to play a version of the classic Countdown Game.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

This task follows on from Build it Up and takes the ideas into three dimensions!

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

There are nasty versions of this dice game but we'll start with the nice ones...

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Number problems at primary level to work on with others.