Other tags that relate to Base Puzzle
Diophantine equations. Multiplication & division. Addition & subtraction. Mathematical reasoning & proof. Number bases. Number theory. Creating and manipulating expressions and formulae. Integers. Place value. Factors and multiples.There are 64 results
Broad Topics > Calculations and Numerical Methods > Addition & subtraction
Aba
Age 11 to 14 Challenge Level:
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.
Digit Sum
Age 14 to 16 Short Challenge Level:
What is the sum of all the digits in all the integers from one to one million?
As Easy as 1,2,3
Age 11 to 14 Challenge Level:
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. . . .
Alphabet Soup
Age 11 to 14 Challenge Level:
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.
Tis Unique
Age 11 to 14 Challenge Level:
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.
The Patent Solution
Age 11 to 14 Challenge Level:
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?
Arrange the Digits
Age 11 to 14 Challenge Level:
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?
Subtraction Surprise
Age 7 to 14 Challenge Level:
Try out some calculations. Are you surprised by the results?
Double Digit
Age 11 to 14 Challenge Level:
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. . . .
Diagonal Sums
Age 7 to 14 Challenge Level:
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?
Largest Number
Age 11 to 14 Challenge Level:
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.
Two and Two
Age 11 to 16 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Adding All Nine
Age 11 to 14 Challenge Level:
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. . . .
Multiply the Addition Square
Age 11 to 14 Challenge Level:
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?
Pairs
Age 11 to 14 Challenge Level:
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
Cayley
Age 11 to 14 Challenge Level:
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Jugs of Wine
Age 11 to 14 Challenge Level:
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
Score
Age 11 to 14 Challenge Level:
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. . . .
Crossed Ends
Age 11 to 14 Challenge Level:
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Magic Squares for Special Occasions
Age 11 to 16
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.
Eight Dominoes
Age 7 to 16 Challenge Level:
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
Football Sum
Age 11 to 14 Challenge Level:
Find the values of the nine letters in the sum: FOOT + BALL = GAME
And So on and So On
Age 11 to 14 Challenge Level:
If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?
Number Pyramids
Age 11 to 14 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Got it Article
Age 7 to 14
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
3388
Age 11 to 14 Challenge Level:
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.
Adding and Subtracting Positive and Negative Numbers
Age 11 to 14
How can we help students make sense of addition and subtraction of negative numbers?
Making Sense of Positives and Negatives
Age 11 to 14
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Alphabetti Sudoku
Age 11 to 16 Challenge Level:
This Sudoku requires you to do some working backwards before working forwards.
Nice or Nasty for Two
Age 7 to 14 Challenge Level:
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Postage
Age 14 to 16 Challenge Level:
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. . . .
Making Maths: Double-sided Magic Square
Age 7 to 14 Challenge Level:
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Countdown
Age 7 to 14 Challenge Level:
Here is a chance to play a version of the classic Countdown Game.
Cinema Problem
Age 11 to 14 Challenge Level:
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.
Pole Star Sudoku 2
Age 11 to 16 Challenge Level:
This Sudoku, based on differences. Using the one clue number can you find the solution?
Twenty20
Age 7 to 16 Challenge Level:
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Magic Letters
Age 11 to 14 Challenge Level:
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 for Two
Age 7 to 14 Challenge Level:
Got It game for an adult and child. How can you play so that you know you will always win?
Consecutive Negative Numbers
Age 11 to 14 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Charitable Pennies
Age 7 to 14 Challenge Level:
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Weights
Age 11 to 14 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
An Introduction to Magic Squares
Age 7 to 16
Find out about Magic Squares in this article written for students. Why are they magic?!
Have You Got It?
Age 11 to 14 Challenge Level:
Can you explain the strategy for winning this game with any target?
Calendar Capers
Age 11 to 14 Challenge Level:
Choose any three by three square of dates on a calendar page...
Pair Sums
Age 11 to 14 Challenge Level:
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Number Daisy
Age 11 to 14 Challenge Level:
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.