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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This Sudoku requires you to do some working backwards before working forwards.
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?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you substitute numbers for the letters in these sums?
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.
Number problems at primary level that require careful consideration.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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
Find out about Magic Squares in this article written for students. Why are they magic?!
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
Can you work out some different ways to balance this equation?
What happens when you round these three-digit numbers to the nearest 100?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Follow the clues to find the mystery number.
A little mouse called Delia lives in a hole in the bottom of a
tree.....How many days will it be before Delia has to take the same
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?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?