Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The idea of this game is to add or subtract the two numbers on the
dice and cover the result on the grid, trying to get a line of
three. Are there some numbers that are good to aim for?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?"
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Charlie and Lynne 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
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 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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
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?
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.
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you substitute numbers for the letters in these sums?
Find out about Magic Squares in this article written for students. Why are they magic?!
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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. . . .
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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