A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

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

Use the differences to find the solution to this Sudoku.

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. . . .

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

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?

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

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

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

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.

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

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.

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

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

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?

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?

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

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.

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

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.

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

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.

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

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.

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

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits

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

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

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

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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.

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?

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

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

What is the smallest perfect square that ends with the four digits 9009?

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

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?

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

A Sudoku with clues given as sums of entries.

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.