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?

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?

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.

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?

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?

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

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.

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

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

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?

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

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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.?

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

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.

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?

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

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

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.

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

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?

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

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.

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.

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.

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?"

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

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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

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

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

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.

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.

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

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.

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

Use the differences to find the solution to this Sudoku.

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 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. . . .

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

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?

A few extra challenges set by some young NRICH members.

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

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 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. . . .