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?

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

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

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

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.

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 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?

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

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.

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?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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.

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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!

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

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

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

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

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.

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

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

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?

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

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.

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

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

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?

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

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.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.