Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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

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

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....?

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

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?

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

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.

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

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

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?

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

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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

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

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?

How many possible necklaces can you find? And how do you know you've found them all?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

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!

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

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

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?

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

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

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?

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.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Investigate the different ways you could split up these rooms so that you have double the number.

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

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

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

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?