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. . . .

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?

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?

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

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

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?"

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

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

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?

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

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

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.

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?

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

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

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

Can you use this information to work out Charlie's house number?

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?

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.

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

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?

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?

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.

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?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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!

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.