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

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?

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

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

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

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

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

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

How long does it take to brush your teeth? Can you find the matching length of time?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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.

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

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.

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?

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

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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

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.

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.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

This challenge is about finding the difference between numbers which have the same tens digit.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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.?

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

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?