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 find the chosen number from the grid using the clues?

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

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?

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....?

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 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?

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.

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

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?

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

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?

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 how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

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?

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

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

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

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

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

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?

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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?

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

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

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

Number problems at primary level that require careful consideration.

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?

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?

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

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