Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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?

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

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

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

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

A Sudoku based on clues that give the differences between adjacent cells.

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 few extra challenges set by some young NRICH members.

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.

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

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

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?

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

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.

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?

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

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

A Sudoku that uses transformations as supporting clues.

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.

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

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

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?

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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.

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

A Sudoku with clues given as sums of entries.

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.

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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

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?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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

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

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?

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

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.

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