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?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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 replace the letters with numbers? Is there only one
solution in each case?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
This Sudoku, based on differences. Using the one clue number can you find the solution?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How many different symmetrical shapes can you make by shading triangles or squares?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
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?
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. . . .
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you substitute numbers for the letters in these sums?
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?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.