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 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. . . .
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?
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten 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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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. . . .
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Four friends must cross a bridge. How can they all cross it in just
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Given the products of adjacent cells, can you complete this Sudoku?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Given the products of diagonally opposite cells - can you complete
A Sudoku that uses transformations as supporting clues.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find 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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.