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?
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?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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?
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Find out about Magic Squares in this article written for students. Why are they magic?!
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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?
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 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.
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.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
A Sudoku that uses transformations as supporting clues.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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 pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Two sudokus in one. Challenge yourself to make the necessary
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
This challenge extends the Plants investigation so now four or more children are involved.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
A Sudoku with a twist.
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.
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 package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Use the differences to find the solution to this Sudoku.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".