Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

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

Given the products of adjacent cells, can you complete this Sudoku?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

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

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

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Number problems at primary level that require careful consideration.

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?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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?

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

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing 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?

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?

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

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

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

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?