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?

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.

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?

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

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

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

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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

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

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

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

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?

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.

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

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.

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?

You need to find the values of the stars before you can apply normal Sudoku rules.

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

A Sudoku that uses transformations as supporting clues.

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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

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?

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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

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

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.

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 have "double vision" - two Sudoku's for the price of one

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.

A Sudoku with clues given as sums of entries.

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.

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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.

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. . . .

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