Label this plum tree graph to make it totally magic!
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
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
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?
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four
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 Sudoku with clues as ratios.
A pair of Sudoku puzzles that together lead to a complete solution.
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 that uses transformations as supporting clues.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Find out about Magic Squares in this article written for students. Why are they magic?!
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Two sudokus in one. Challenge yourself to make the necessary
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?
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?
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 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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
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?