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!

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

A game for 2 players. Practises subtraction or other maths operations knowledge.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Can you substitute numbers for the letters in these sums?

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!

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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?

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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.

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?

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

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?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Find the sum of all three-digit numbers each of whose digits is odd.

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!

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 arrange 5 different digits (from 0 - 9) in the cross in the way described?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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.