# Resources tagged with: Modular arithmetic

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### There are 30 results

Broad Topics > Properties of Numbers > Modular arithmetic ### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now? ### More Mods

##### Age 14 to 16Challenge Level

What is the units digit for the number 123^(456) ? ### An Introduction to Modular Arithmetic

##### Age 14 to 16

An introduction to the notation and uses of modular arithmetic ### Differences

##### Age 11 to 14Challenge Level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number? ### Novemberish

##### Age 14 to 16Challenge 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. ### Transposition Fix

##### Age 14 to 16Challenge 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 Codes

##### Age 14 to 16Challenge 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. . . . ### Going Round in Circles

##### Age 11 to 14Challenge Level

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be? ### A One in Seven Chance

##### Age 11 to 14Challenge Level

What is the remainder when 2^{164}is divided by 7? ### Odd Stones

##### Age 14 to 16Challenge Level

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed. ### Two Much

##### Age 11 to 14Challenge Level

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears. ### Mod 3

##### Age 14 to 16Challenge Level

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3. ### Knapsack

##### Age 14 to 16Challenge Level

You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value. ### Take Three from Five

##### Age 14 to 16Challenge 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? ### Check Code Sensitivity

##### Age 14 to 16Challenge 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. ### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make? ### Elevenses

##### Age 11 to 14Challenge 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 16Challenge Level

Which numbers can we write as a sum of square numbers? ### Zeller's Birthday

##### Age 14 to 16Challenge Level

What day of the week were you born on? Do you know? Here's a way to find out. ### Round and Round and Round

##### Age 11 to 14Challenge Level

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help? ### The Chinese Remainder Theorem

##### Age 14 to 18

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5." ### 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. ### How Much Can We Spend?

##### Age 11 to 14Challenge 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? ### Obviously?

##### Age 14 to 18Challenge Level

Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6. ### Days and Dates

##### Age 11 to 14Challenge Level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after... ### Euler's Officers

##### Age 14 to 16Challenge Level

How many different ways can you arrange the officers in a square? ### Where Can We Visit?

##### Age 11 to 14Challenge 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? ### Grid Lockout

##### Age 14 to 16Challenge Level

What remainders do you get when square numbers are divided by 4? ### Guesswork

##### Age 14 to 16Challenge 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. ### The Best Card Trick?

##### Age 11 to 16Challenge 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?