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.

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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

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

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

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. . . .

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

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

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

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

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

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 Sudoku that uses transformations as supporting clues.

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.

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

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.

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

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.

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

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

A Sudoku with clues given as sums of entries.

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

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

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

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.

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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

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.

Use the differences to find the solution to 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?

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.

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?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?