Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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.

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?

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

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.

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

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?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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!

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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.

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

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!

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?

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?

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Use the number weights to find different ways of balancing the equaliser.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

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 hang weights in the right place to make the equaliser balance?

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.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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.

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.

An environment which simulates working with Cuisenaire rods.

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?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

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?