Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
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.
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
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.
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?
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.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Can you use the information to find out which cards I have used?
How many different triangles can you make on a circular pegboard that has nine pegs?
What could the half time scores have been in these Olympic hockey matches?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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?
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.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Can you cover the camel with these pieces?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?