During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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

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

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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?

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

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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

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

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?

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.

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

Can you use the information to find out which cards I have used?

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

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 second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Use the differences to find the solution to this Sudoku.

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?"

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.

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

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

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

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. . . .

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?

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

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.

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.

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

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. . . .

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?

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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. . . .

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

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

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