Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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?
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
A few extra challenges set by some young NRICH members.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite 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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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 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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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 man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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 second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku with clues as ratios or fractions.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Four small numbers give the clue to the contents of the four
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A pair of Sudoku puzzles that together lead to a complete solution.
Given the products of adjacent cells, can you complete this Sudoku?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with a twist.
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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
A Sudoku with clues given as sums of entries.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
This challenge extends the Plants investigation so now four or more children are involved.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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.