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Resources tagged with Factors and multiples similar to Weekly Problem 48 - 2006:

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Broad Topics > Numbers and the Number System > Factors and multiples

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Adding in Rows

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

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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Repeaters

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Adding All Nine

Stage: 3 Challenge Level: Challenge Level:1

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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Got It

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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What Numbers Can We Make?

Stage: 3 Challenge Level: Challenge Level:1

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

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Special Sums and Products

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

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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Reverse to Order

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

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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Even So

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

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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Three Times Seven

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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Hidden Squares

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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GOT IT Now

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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What Numbers Can We Make Now?

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Take Three from Five

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Product Sudoku

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

The clues for this Sudoku are the product of the numbers in adjacent squares.

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LCM Sudoku II

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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Ben's Game

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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Funny Factorisation

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

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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Cuboids

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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Dozens

Stage: 3 Challenge Level: Challenge Level:1

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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American Billions

Stage: 3 Challenge Level: Challenge Level:1

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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14 Divisors

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

What is the smallest number with exactly 14 divisors?

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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What Do You Need?

Stage: 2 Challenge Level: Challenge Level:1

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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Shifting Times Tables

Stage: 3 Challenge Level: Challenge Level:1

Can you find a way to identify times tables after they have been shifted up?

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Remainder

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

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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Crossings

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

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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Can You Find a Perfect Number?

Stage: 2 and 3

Can you find any perfect numbers? Read this article to find out more...

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Product Sudoku 2

Stage: 3 and 4 Challenge Level: Challenge Level:1

Given the products of diagonally opposite cells - can you complete this Sudoku?

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Round and Round the Circle

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

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Stars

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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The Remainders Game

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

A game that tests your understanding of remainders.

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Three Dice

Stage: 2 Challenge Level: Challenge Level:1

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Three Neighbours

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

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

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Substitution Cipher

Stage: 3 and 4 Challenge Level: Challenge Level:1

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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Substitution Transposed

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

Substitution and Transposition all in one! How fiendish can these codes get?

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Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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Power Crazy

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

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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Helen's Conjecture

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

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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Transposition Cipher

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you work out what size grid you need to read our secret message?

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Inclusion Exclusion

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

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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Down to Nothing

Stage: 2 Challenge Level: Challenge Level:1

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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Number Tracks

Stage: 2 Challenge Level: Challenge Level:1

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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Colour Wheels

Stage: 2 Challenge Level: Challenge Level:1

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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Eminit

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

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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Big Powers

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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Multiply Multiples 3

Stage: 2 Challenge Level: Challenge Level:1

Have a go at balancing this equation. Can you find different ways of doing it?

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A First Product Sudoku

Stage: 3 Challenge Level: Challenge Level:1

Given the products of adjacent cells, can you complete this Sudoku?

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Multiply Multiples 2

Stage: 2 Challenge Level: Challenge Level:1

Can you work out some different ways to balance this equation?

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Multiply Multiples 1

Stage: 2 Challenge Level: Challenge Level:1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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Sieve of Eratosthenes

Stage: 3 Challenge Level: Challenge Level:1

Follow this recipe for sieving numbers and see what interesting patterns emerge.