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.

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?

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

A Sudoku that uses transformations as supporting clues.

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

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

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

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?

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

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

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

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

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

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.

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

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

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.

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

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.

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

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

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.

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.

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

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?

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

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

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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.

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 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.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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

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.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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?

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?

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.