Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

An investigation that gives you the opportunity to make and justify predictions.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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?

Can you find the chosen number from the grid using the clues?

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

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

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?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

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.

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

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?

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?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Can you make square numbers by adding two prime numbers together?

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 the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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?

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?