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.

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?

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

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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

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 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?

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

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

Use the differences to find the solution to this Sudoku.

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

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

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.

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

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

A Sudoku that uses transformations as supporting clues.

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

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?

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

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

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

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

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

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 challenge extends the Plants investigation so now four or more children are involved.

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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!

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

A challenging activity focusing on finding all possible ways of stacking rods.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Given the products of adjacent cells, can you complete this Sudoku?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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?

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