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.

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?

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

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

A few extra challenges set by some young NRICH members.

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.

A challenging activity focusing on finding all possible ways of stacking rods.

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

You need to find the values of the stars before you can apply normal Sudoku rules.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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

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

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

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?

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

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

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

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?

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

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.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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

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

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

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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.

An activity making various patterns with 2 x 1 rectangular tiles.

Given the products of adjacent cells, can you complete this Sudoku?