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

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

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

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.

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

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?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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

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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

What is the best way to shunt these carriages so that each train can continue its journey?

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

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

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?

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

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?

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

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?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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.

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?

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?

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

How many different rectangles can you make using this set of rods?

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

What happens when you try and fit the triomino pieces into these two grids?