This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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?

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?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

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

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?"

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

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

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?

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

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

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

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

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?

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?

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

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?

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

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

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

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?

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

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

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

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

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?

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?

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.

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?

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.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.