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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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 values of the nine letters in the sum: FOOT + BALL = GAME
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.
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?
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...
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. . . .
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
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?
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.
A few extra challenges set by some young NRICH members.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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. . . .
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
This Sudoku, based on differences. Using the one clue number can you find the solution?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the clues about the shaded areas to help solve this sudoku
This Sudoku combines all four arithmetic operations.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Can you coach your rowing eight to win?
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.