If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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?

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?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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

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.

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 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.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Find out about Magic Squares in this article written for students. Why are they magic?!

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Investigate the different ways you could split up these rooms so that you have double the number.

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?