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 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?
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?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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 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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
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.
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...
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.
If you are given the mean, median and mode of five positive whole
numbers, can you find the numbers?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
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?
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 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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios.
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
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku that uses transformations as supporting clues.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
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?
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 Sudoku with a twist.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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.
Use the differences to find the solution to this Sudoku.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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?