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.

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

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

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?

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

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

What happens when you round these three-digit numbers to the nearest 100?

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

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

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Number problems at primary level that require careful consideration.

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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 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 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?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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.

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 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!

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

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

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

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

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

Can you replace the letters with numbers? Is there only one solution in each case?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

Can you make square numbers by adding two prime numbers together?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

An investigation that gives you the opportunity to make and justify predictions.

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 challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

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?

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

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