Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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 make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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?

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?

How many different rhythms can you make by putting two drums on the wheel?

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?

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?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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....?

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?

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

Can you replace the letters with numbers? Is there only one solution in each case?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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?

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

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.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

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

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

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you fill in the empty boxes in the grid with the right shape and colour?

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

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

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

Number problems at primary level that require careful consideration.

Can you find all the different ways of lining up these Cuisenaire rods?

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?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Find all the numbers that can be made by adding the dots on two dice.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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?