Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
A few extra challenges set by some young NRICH members.
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?
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. . . .
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.
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?
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 arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?"
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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. . . .
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
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?
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Two sudokus in one. Challenge yourself to make the necessary
Four small numbers give the clue to the contents of the four
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
In this matching game, you have to decide how long different events take.
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 challenge extends the Plants investigation so now four or more children are involved.
Use the differences to find the solution to this Sudoku.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
A Sudoku that uses transformations as supporting clues.