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?

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

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.

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

What could the half time scores have been in these Olympic hockey matches?

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?

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

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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?"

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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

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

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

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

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

How many different rectangles can you make using this set of rods?

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?

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

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?