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

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

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

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?

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

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

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?

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?

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

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

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

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?

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

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?

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

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....?

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

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?

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

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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

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

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

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

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

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?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Number problems for lower primary that will get you thinking.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Try this matching game which will help you recognise different ways of saying the same time interval.

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

How many different rectangles can you make using this set of rods?