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

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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?

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?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Use the clues about the shaded areas to help solve 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?

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?"

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?

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

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?

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

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.

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

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.

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

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

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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.

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

A Sudoku that uses transformations as supporting clues.

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

Use the differences to find the solution to this Sudoku.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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

Two sudokus in one. Challenge yourself to make the necessary connections.

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.

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

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.

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.

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Two sudokus in one. Challenge yourself to make the necessary connections.

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .