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. . . .
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?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Replace each letter with a digit to make this addition correct.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
Can you explain how this card trick works?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you explain the strategy for winning this game with any target?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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. . . .
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.
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. . . .
Here is a chance to play a version of the classic Countdown Game.
Here is a chance to play a fractions version of the classic Countdown Game.
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Try out some calculations. Are you surprised by the results?
Choose any three by three square of dates on a calendar page...
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.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Delight your friends with this cunning trick! Can you explain how it works?
This Sudoku requires you to do some working backwards before working forwards.
What is the sum of all the digits in all the integers from one to one million?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
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 numbers in this sum
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.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
How is it possible to predict the card?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .
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?
This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.