Other tags that relate to Base Puzzle
Place value. Integers. Diophantine equations. Number bases. Addition & subtraction. Factors and multiples. Multiplication & division. Creating and manipulating expressions and formulae. Simultaneous equations. Mathematical reasoning & proof.There are 73 results
Broad Topics > Calculations and Numerical Methods > Addition & subtraction
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?
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?
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.
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. . . .
Forwards Add Backwards
Age 11 to 14
Challenge Level
What happens when you add a three digit number to its reverse?
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?
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?
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?
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.
Can You Make 100?
Age 11 to 14
Challenge Level
How many ways can you find to put in operation signs (+ - x ÷) to make 100?
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. . . .
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.
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.
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"?
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. . . .
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. . . .
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
Add to 200
Age 11 to 14
Challenge Level
By selecting digits for an addition grid, what targets can you make?
Football Sum
Age 11 to 14
Challenge Level
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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. . . .
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?
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.
Up, Down, Flying Around
Age 11 to 14
Challenge Level
Play this game to learn about adding and subtracting positive and negative numbers
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.
Difference Sudoku
Age 14 to 16
Challenge Level
Use the differences to find the solution to this Sudoku.
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?
Nice or Nasty
Age 7 to 14
Challenge Level
There are nasty versions of this dice game but we'll start with the nice ones...
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?
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?
Alphabetti Sudoku
Age 11 to 16
Challenge Level
This Sudoku requires you to do some working backwards before working forwards.
Charitable Pennies
Age 7 to 14
Challenge Level
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
More Plant Spaces
Age 7 to 14
Challenge Level
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.
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?
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.
More Children and Plants
Age 7 to 14
Challenge Level
This challenge extends the Plants investigation so now four or more children are involved.
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?
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.
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?
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.
Countdown Fractions
Age 11 to 16
Challenge Level
Here is a chance to play a fractions version of the classic Countdown Game.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.