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

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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

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

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

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?

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.

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

A Sudoku that uses transformations as supporting clues.

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.

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?

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

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

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. . . .

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

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!

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

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?

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

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

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.

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?

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

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 do some working backwards before working forwards.

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

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

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

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

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

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

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

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

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.

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

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.

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

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

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.