Number problems at primary level that require careful consideration.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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?

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

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

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Have a go at balancing this equation. Can you find different ways of doing it?

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?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

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?

This task follows on from Build it Up and takes the ideas into three dimensions!

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

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?

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

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

This dice train has been made using specific rules. How many different trains can you make?

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?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

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

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?

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?

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?

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?

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?

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.

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

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.

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?

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

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?