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

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

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?

What could the half time scores have been in these Olympic hockey matches?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

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.

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

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

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

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

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.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

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

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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?

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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?

What two-digit numbers can you make with these two dice? What can't you make?

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

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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

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

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?