If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

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....?

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

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

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

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?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

In this matching game, you have to decide how long different events take.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

Can you use this information to work out Charlie's house number?

What happens when you try and fit the triomino pieces into these two grids?

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

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?

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?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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

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

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

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.

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

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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

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.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

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

You have 5 darts and your target score is 44. How many different ways could you score 44?