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?
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?
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?
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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 article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Use the differences to find the solution to this Sudoku.
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku with a twist.
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.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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.
A Sudoku with clues as ratios or fractions.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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.
A Sudoku with clues given as sums of entries.
Find out about Magic Squares in this article written for students. Why are they magic?!
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku based on clues that give the differences between adjacent cells.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind