Resources tagged with: Modular arithmetic

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Broad Topics > Properties of Numbers > Modular arithmetic

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?

More Mods

Age 14 to 16
Challenge 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 14
Challenge 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 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.

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 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. . . .

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?

A One in Seven Chance

Age 11 to 14
Challenge Level

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

Odd Stones

Age 14 to 16
Challenge 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 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.

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.

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.

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?

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.

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?

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.

Round and Round and Round

Age 11 to 14
Challenge 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 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?

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.

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...

Euler's Officers

Age 14 to 16
Challenge Level

How many different ways can you arrange the officers in a square?

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?

Grid Lockout

Age 14 to 16
Challenge Level

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

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.

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?