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.

What is the smallest perfect square that ends with the four digits 9009?

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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

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

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

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.

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.

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.

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.

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

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?

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?

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

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

Solve the equations to identify the clue numbers in this Sudoku problem.

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?

The challenge is to find the values of the variables if you are to solve this Sudoku.

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

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

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

Use the differences to find the solution to this Sudoku.

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

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

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

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

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

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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

Use the clues about the shaded areas to help solve this sudoku

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

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.

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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 based on clues that give the differences between adjacent cells.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

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

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!