Resources tagged with Modulus arithmetic similar to A One in Seven Chance:
Other tags that relate to A One in Seven Chance
Divisibility. Number theory. Multiplication & division. Factors and multiples. Generalising. Addition & subtraction. Patterned numbers. Properties of numbers. Modulus arithmetic. Mathematical reasoning & proof.There are 27 results
Broad Topics > Numbers and the Number System > Modulus arithmetic
A One in Seven Chance
Age 11 to 14 Challenge Level:
What is the remainder when 2^{164}is divided by 7?
Going Round in Circles
Age 11 to 14 Challenge Level:
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Mod 3
Age 14 to 16 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Differences
Age 11 to 14 Challenge Level:
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Elevenses
Age 11 to 14 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Filling the Gaps
Age 14 to 16 Challenge Level:
Which numbers can we write as a sum of square numbers?
Zeller's Birthday
Age 14 to 16 Challenge Level:
What day of the week were you born on? Do you know? Here's a way to find out.
What Numbers Can We Make Now?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Latin Squares
Age 11 to 18
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
Take Three from Five
Age 14 to 16 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Transposition Fix
Age 14 to 16 Challenge Level:
Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine. . . .
Check Code Sensitivity
Age 14 to 16 Challenge Level:
You are given the method used for assigning certain check codes and you have to find out if an error in a single digit can be identified.
Two Much
Age 11 to 14 Challenge Level:
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Knapsack
Age 14 to 16 Challenge Level:
You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
Obviously?
Age 14 to 18 Challenge Level:
Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
Check Codes
Age 14 to 16 Challenge Level:
Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check. . . .
What Numbers Can We Make?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Novemberish
Age 14 to 16 Challenge Level:
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
Grid Lockout
Age 14 to 16 Challenge Level:
What remainders do you get when square numbers are divided by 4?
How Much Can We Spend?
Age 11 to 14 Challenge Level:
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Days and Dates
Age 11 to 14 Challenge Level:
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Clock Squares
Age 11 to 14 Challenge Level:
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
Where Can We Visit?
Age 11 to 14 Challenge Level:
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?
Guesswork
Age 14 to 16 Challenge Level:
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Euler's Officers
Age 14 to 16 Challenge Level:
How many different ways can you arrange the officers in a square?
The Best Card Trick?
Age 11 to 16 Challenge Level:
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
NRICH is part of the family of activities in the Millennium Mathematics Project.