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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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 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?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
Use the differences to find the solution to this Sudoku.
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...
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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?
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.
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.
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?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Label this plum tree graph to make it totally magic!
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.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Find out about Magic Squares in this article written for students. Why are they magic?!
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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.
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Can you coach your rowing eight to win?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.