A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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.

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

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

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

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.

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?

A few extra challenges set by some young NRICH members.

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

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

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

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

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

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.

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?

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.

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

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

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?

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?

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.

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?"

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

In this matching game, you have to decide how long different events take.

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.

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?