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?
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?
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 challenging activity focusing on finding all possible ways of stacking rods.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
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 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.
Find out what a "fault-free" rectangle is and try to make some of
A Sudoku with clues as ratios.
A Sudoku with a twist.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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 that uses transformations as supporting clues.
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
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?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
A Sudoku with clues as ratios or fractions.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Can you find all the different triangles on these peg boards, and
find their angles?
You need to find the values of the stars before you can apply normal Sudoku rules.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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 few extra challenges set by some young NRICH members.
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
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.
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?