Find out about Magic Squares in this article written for students. Why are they magic?!
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?
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?
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?
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?
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.
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?
Take three whole numbers. The differences between them give you
three new numbers. Find the differences between the new numbers and
keep repeating this. What happens?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
A pair of Sudoku puzzles that together lead to a complete solution.
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 pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Use the differences to find the solution to this Sudoku.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Four small numbers give the clue to the contents of the four
A Sudoku with a twist.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Two sudokus in one. Challenge yourself to make the necessary
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
This Sudoku combines all four arithmetic operations.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
Use the clues about the shaded areas to help solve this sudoku
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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?
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. . . .
Can you coach your rowing eight to win?
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.