Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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 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.

This challenge extends the Plants investigation so now four or more children are involved.

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.

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?

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.

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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

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?

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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

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

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

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?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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 do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Can you find all the different triangles on these peg boards, and find their angles?

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?

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

A few extra challenges set by some young NRICH members.

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....?

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Can you find all the different ways of lining up these Cuisenaire rods?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

How many different triangles can you make on a circular pegboard that has nine pegs?