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

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?

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

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?

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

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

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

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!

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

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?

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.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

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!

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

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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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 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?

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!

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?

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

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

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

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.

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.

An environment which simulates working with Cuisenaire rods.

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

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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?

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?

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?

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

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?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

This challenge extends the Plants investigation so now four or more children are involved.

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

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?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?