Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
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?"
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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.
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?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
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?
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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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...
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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 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?
Use the differences to find the solution to this Sudoku.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Take three whole numbers. The differences between them give you
three new numbers. Find the differences between the new numbers and
keep repeating this. What happens?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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?
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.
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.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
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.
This challenge extends the Plants investigation so now four or more children are involved.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?