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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
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?
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...
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Use the differences to find the solution to this Sudoku.
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!
This Sudoku requires you to do some working backwards before working forwards.
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?
A Sudoku with clues as ratios.
A Sudoku with a twist.
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
This Sudoku, based on differences. Using the one clue number can you find the solution?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Two sudokus in one. Challenge yourself to make the necessary
Four small numbers give the clue to the contents of the four
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A pair of Sudoku puzzles that together lead to a complete solution.
You need to find the values of the stars before you can apply normal Sudoku rules.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues given as sums of entries.
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.
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?
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?
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?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.