Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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.

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

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.

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

In how many ways can you stack these rods, following the rules?

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.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

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 use the information to find out which cards I have used?

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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

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

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.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.