Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
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.?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
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?
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.
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?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Investigate the different ways you could split up these rooms so that you have double the number.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared 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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you find all the different ways of lining up these Cuisenaire rods?
Can you use the information to find out which cards I have used?
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.
How many models can you find which obey these rules?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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 could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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 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.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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?