This Sudoku, based on differences. Using the one clue number can you find the solution?

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?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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?"

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

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

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

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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

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

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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. . . .

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?

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

Four small numbers give the clue to the contents of the four surrounding cells.

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

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?

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

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?

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

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?

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

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.

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?

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

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.

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

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?

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?

A Sudoku that uses transformations as supporting clues.

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?

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

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

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?

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?

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.

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?

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?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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

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