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

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

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?"

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...

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.

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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

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.

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?

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

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?

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.

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?

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.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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

A few extra challenges set by some young NRICH members.

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?

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?

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.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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?

A pair of Sudoku puzzles that together lead to a complete solution.

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

Use the differences to find the solution to this Sudoku.

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

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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 about the shaded areas to help solve this sudoku

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

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.

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

This Sudoku requires you to do some working backwards before working forwards.

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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

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

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

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?

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

Find out about Magic Squares in this article written for students. Why are they magic?!

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

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

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.