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

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?

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?

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?

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

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

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.

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

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?

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?

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

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

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

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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.

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

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Can you find out in which order the children are standing in this 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.

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?

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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

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?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Number problems for lower primary that will get you thinking.

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

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

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?

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?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

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

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

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.