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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Find out what a "fault-free" rectangle is and try to make some of
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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 different symmetrical shapes can you make by shading triangles or squares?
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.
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.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
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?
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"?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
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.
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. . . .
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?
Can you find all the different ways of lining up these Cuisenaire
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.
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.
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. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A few extra challenges set by some young NRICH members.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.