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

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

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

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

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?

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 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?

Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

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.

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

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.

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

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build 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?

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

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.

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?

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

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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?

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?

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

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

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....?

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

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.?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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?

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?

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

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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

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.

The pages of my calendar have got mixed up. Can you sort them out?

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

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?

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.