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.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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.

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 Sudoku puzzles that together lead to a complete solution.

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

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

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. . . .

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

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

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?

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

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

A Sudoku that uses transformations as supporting clues.

A Sudoku with clues given as sums of entries.

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

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?

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

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

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

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

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?

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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.

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

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?

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

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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?

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.

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

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

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

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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.

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.

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

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.

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

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?