Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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

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?

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

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.

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

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

A Sudoku that uses transformations as supporting clues.

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

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.

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

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.

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

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?

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

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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

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

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?

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 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.

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

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?

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

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?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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.

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

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. . . .