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

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

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

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

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.

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?

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

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

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

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

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.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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?

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?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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?

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.

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

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

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

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

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

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

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

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

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.

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?

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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?

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?

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?

Can you work out some different ways to balance this equation?

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.

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.

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

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

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?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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?

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.