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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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?

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

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

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

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

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

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?

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

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?

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....?

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

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

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?

In this matching game, you have to decide how long different events take.

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

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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?

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

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

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

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

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

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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.

This challenge extends the Plants investigation so now four or more children are involved.

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

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?

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!

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

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

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?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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

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?

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.