Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

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

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.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

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?

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

The Zargoes use almost the same alphabet as English. What does this birthday message say?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

How many trapeziums, of various sizes, are hidden in this picture?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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 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!

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?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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

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

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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?

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

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

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?

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!