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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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. . . .
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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 Sudoku with a twist.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Use the differences to find the solution to this Sudoku.
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Four small numbers give the clue to the contents of the four
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the clues about the shaded areas to help solve this sudoku
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many different symmetrical shapes can you make by shading triangles or squares?
Label this plum tree graph to make it totally magic!
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku combines all four arithmetic operations.
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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A pair of Sudoku puzzles that together lead to a complete solution.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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 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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku with clues as ratios.