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Resources tagged with Modulus arithmetic similar to Divisibility Tests:

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Check Code Sensitivity

Stage: 4 Challenge Level: Challenge Level:1

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.

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Latin Squares

Stage: 2, 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.

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Modular Arithmetic

Stage: 4

An introduction to the notation and uses of modular arithmetic

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Check Codes

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Transposition Fix

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Knapsack

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Grid Lockout

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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More Mods

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the units digit for the number 123^(456) ?

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Obviously?

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

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Zeller's Birthday

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Euler's Officers

Stage: 4 Challenge Level: Challenge Level:1

How many different solutions can you find to this problem? Arrange 25 officers, each having one of five different ranks a, b, c, d and e, and belonging to one of five different regiments p, q, r, s. . . .

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Days and Dates

Stage: 4 Challenge Level: Challenge Level:1

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

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Differences

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Mod 3

Stage: 4 Challenge Level: Challenge Level:1

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

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Novemberish

Stage: 4 Challenge Level: Challenge Level:1

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.

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Clock Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.

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A One in Seven Chance

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Where Can We Visit?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Charlie and Lynne 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?

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Elevenses

Stage: 3 Challenge Level: Challenge Level:1

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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Take Three from Five

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you guarantee that from any group of 5 numbers it is always possible to choose three numbers that will add up to a multiple of 3?

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Two Much

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Prime AP

Stage: 4 Challenge Level: Challenge Level:1

Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference is divisible by 6. What if one of the terms is 3?

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Guesswork

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Going Round in Circles

Stage: 3 Challenge Level: Challenge Level:1

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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How Much Can We Spend?

Stage: 3 Challenge Level: Challenge Level:1

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?