How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

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

Here is a chance to play a version of the classic Countdown Game.

Number problems at primary level that require careful consideration.

If you have only four weights, where could you place them in order to balance this equaliser?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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?

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.

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

A game for 2 players. Practises subtraction or other maths operations knowledge.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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.

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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!

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Investigate what happens when you add house numbers along a street in different ways.

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Investigate the different distances of these car journeys and find out how long they take.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?