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

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

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

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?

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.

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?

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?

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?

My coat has three buttons. How many ways can you find to do up all the buttons?

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

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

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

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

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?

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

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?

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.

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

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.

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?

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?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

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?

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.

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

What could the half time scores have been in these Olympic hockey matches?

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

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?

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?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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

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?

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

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Have a go at balancing this equation. Can you find different ways of doing it?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Find all the numbers that can be made by adding the dots on two dice.

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?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

An investigation that gives you the opportunity to make and justify predictions.

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