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.
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...
The clues for this Sudoku are the product of the numbers in adjacent squares.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?"
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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?
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 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?
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
You have twelve weights, one of which is different from the rest.
Using just 3 weighings, can you identify which weight is the odd
one out, and whether it is heavier or lighter than the rest?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
Use the differences to find the solution to this Sudoku.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
Label this plum tree graph to make it totally magic!
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.
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?