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

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

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 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.

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

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?

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?

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

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

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

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

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

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

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

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?

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 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?

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?

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.

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.?

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

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

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

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

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

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?

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?

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?

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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?

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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?

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

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?

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

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

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.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

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