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.

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?

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.

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.

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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

A few extra challenges set by some young NRICH members.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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?

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. . . .

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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.

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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?

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?

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.

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. . . .

Find out about Magic Squares in this article written for students. Why are they magic?!