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

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.

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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

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

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?

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

Have a go at balancing this equation. Can you find different ways of doing it?

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?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you 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?

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

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

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

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

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?

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

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

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

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

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

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

Can you work out some different ways to balance this equation?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

What happens when you round these three-digit numbers to the nearest 100?

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?

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?

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?

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

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....?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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

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

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