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.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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

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?

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

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.

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?

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

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?

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?

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

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 task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

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

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 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?

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

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!

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

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

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

How many trapeziums, of various sizes, are hidden in this picture?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

What could the half time scores have been in these Olympic hockey matches?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Can you use this information to work out Charlie's house number?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

In how many ways can you stack these rods, following the rules?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?