Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How long does it take to brush your teeth? Can you find the matching length of time?

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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....?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

This challenge is about finding the difference between numbers which have the same tens digit.

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 information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Can you find out in which order the children are standing in this line?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

My coat has three buttons. How many ways can you find to do up all the buttons?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

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?

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

This task follows on from Build it Up and takes the ideas into three dimensions!

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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.

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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?