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

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?

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?

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

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

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....?

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?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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 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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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.

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?

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

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?

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

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

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

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

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

Number problems at primary level that require careful consideration.

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?

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

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

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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?

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

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

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.