Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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.
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
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.
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. . . .
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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 smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
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.
Given the products of adjacent cells, can you complete this Sudoku?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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. . . .
This Sudoku, based on differences. Using the one clue number can you find the solution?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
Four small numbers give the clue to the contents of the four
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?
Two sudokus in one. Challenge yourself to make the necessary
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...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
Use the differences to find the solution to this Sudoku.
In this matching game, you have to decide how long different events take.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
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?