Label this plum tree graph to make it totally magic!
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.
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 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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
The challenge is to find the values of the variables if you are to
solve this Sudoku.
A Sudoku with a twist.
You need to find the values of the stars before you can apply normal Sudoku rules.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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 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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
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
Solve the equations to identify the clue numbers in this Sudoku 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?
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Four small numbers give the clue to the contents of the four
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
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. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
A Sudoku with clues as ratios.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
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.
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 with clues given as sums of entries.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Two sudokus in one. Challenge yourself to make the necessary
A pair of Sudoku puzzles that together lead to a complete solution.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
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?
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?
An introduction to bond angle geometry.
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 use your powers of logic and deduction to work out the missing information in these sporty situations?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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?
Use the clues about the shaded areas to help solve this sudoku