Resources tagged with Modulus arithmetic similar to A One in Seven Chance:
Other tags that relate to A One in Seven Chance
Factors and multiples. Addition & subtraction. Mathematical reasoning & proof. Properties of numbers. Number theory. Multiplication & division. Generalising. Divisibility. Patterned numbers. Modulus arithmetic.There are 27 results
Broad Topics > Numbers and the Number System > Modulus arithmetic
Differences
Stage: 3 Challenge Level: 
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Elevenses
Stage: 3 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?
Mod 3
Stage: 4 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Going Round in Circles
Stage: 3 Challenge Level:
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
What Numbers Can We Make?
Stage: 3 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Latin Squares
Stage: 3, 4 and 5
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
Stage: 4 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?
Knapsack
Stage: 4 Challenge Level:
You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
Transposition Fix
Stage: 4 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. . . .
Obviously?
Stage: 4 and 5 Challenge Level:
Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
Grid Lockout
Stage: 4 Challenge Level:
What remainders do you get when square numbers are divided by 4?
What Numbers Can We Make Now?
Stage: 3 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Two Much
Stage: 3 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.
Clock Squares
Stage: 3 Challenge Level:
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
Check Codes
Stage: 4 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. . . .
Zeller's Birthday
Stage: 4 Challenge Level:
What day of the week were you born on? Do you know? Here's a way to find out.
Check Code Sensitivity
Stage: 4 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.
Novemberish
Stage: 4 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.
Days and Dates
Stage: 3 Challenge Level:
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Where Can We Visit?
Stage: 3 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?
How Much Can We Spend?
Stage: 3 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?
Guesswork
Stage: 4 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
Stage: 4 Challenge Level:
How many different ways can you arrange the officers in a square?
The Best Card Trick?
Stage: 3 and 4 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.