15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Delight your friends with this cunning trick! Can you explain how it works?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Try out some calculations. Are you surprised by the results?
Play this game to learn about adding and subtracting positive and negative numbers
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
How is it possible to predict the card?
Replace each letter with a digit to make this addition correct.
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Can you explain the strategy for winning this game with any target?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Here is a chance to play a fractions version of the classic Countdown Game.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
This Sudoku, based on differences. Using the one clue number can you find the solution?
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
By selecting digits for an addition grid, what targets can you make?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This Sudoku requires you to do some working backwards before working forwards.
Can you explain how this card trick works?
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
What is the sum of all the digits in all the integers from one to one million?
What happens when you add a three digit number to its reverse?
A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
There are nasty versions of this dice game but we'll start with the nice ones...
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.
Use the differences to find the solution to this Sudoku.
How many different differences can you make?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.
Find out about Magic Squares in this article written for students. Why are they magic?!