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?

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

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

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

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?

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

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?

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

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?

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

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

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

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?

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?

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?

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.

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

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?

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

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

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?

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.

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

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.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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 make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

This article for primary teachers suggests ways in which to help children become better at working systematically.

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.

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

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