The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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

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?

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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.

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.

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?

How many different symmetrical shapes can you make by shading triangles or squares?

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.

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?

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?

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

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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

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.

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

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

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?

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

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?

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.

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

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

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

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

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

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?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Use the clues about the shaded areas to help 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.

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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. . . .

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.