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

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?

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?

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

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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.

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 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?

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.

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 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.

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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

A Sudoku that uses transformations as supporting clues.

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?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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

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.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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?

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

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. . . .

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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.

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

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

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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

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

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.

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

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

A Sudoku based on clues that give the differences between adjacent cells.

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?