Find out about Magic Squares in this article written for students. Why are they magic?!
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.
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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
A Sudoku with a twist.
How many different symmetrical shapes can you make by shading triangles or squares?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
You have twelve weights, one of which is different from the rest.
Using just 3 weighings, can you identify which weight is the odd
one out, and whether it is heavier or lighter than the rest?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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.
Two sudokus in one. Challenge yourself to make the necessary
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
A Sudoku with clues as ratios.
Use the differences to find the solution to this Sudoku.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios or fractions.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
A Sudoku based on clues that give the differences between adjacent cells.
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 Sudoku with clues given as sums of entries.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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?
Label this plum tree graph to make it totally magic!
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
A pair of Sudoku puzzles that together lead to a complete solution.
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.
Four small numbers give the clue to the contents of the four