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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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...
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 arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
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?
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?
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?
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.
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.
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 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?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
How many different symmetrical shapes can you make by shading triangles or squares?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
A few extra challenges set by some young NRICH members.
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 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?"
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. . . .
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Use the differences to find the solution to this Sudoku.
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
An investigation that gives you the opportunity to make and justify
This Sudoku, based on differences. Using the one clue number can you find the solution?
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. . . .
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?