Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
The challenge is to find the values of the variables if you are to
solve this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
This Sudoku requires you to do some working backwards before working forwards.
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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This Sudoku combines all four arithmetic operations.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
Two sudokus in one. Challenge yourself to make the necessary
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Four small numbers give the clue to the contents of the four
Use the differences to find the solution to this Sudoku.
A Sudoku with clues as ratios.
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?