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Resources tagged with Properties of numbers similar to Weekly Problem 16 - 2006:

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Broad Topics > Numbers and the Number System > Properties of numbers

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Times Right

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

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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Thirty Six Exactly

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

The number 12 = 2^2 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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One to Eight

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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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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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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X Marks the Spot

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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Oh! Hidden Inside?

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

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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Happy Octopus

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

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.

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Arrange the Digits

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

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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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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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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Slippy Numbers

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

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

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The Patent Solution

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

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

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Whole Numbers Only

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

Can you work out how many of each kind of pencil this student bought?

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Palindromes

Stage: 1, 2 and 3

Find out about palindromic numbers by reading this article.

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Writ Large

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

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

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Like Powers

Stage: 3 Challenge Level: Challenge Level:1

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

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Please Explain

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

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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Not a Polite Question

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

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

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Factors and Multiple Challenges

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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Water Lilies

Stage: 3 Challenge Level: Challenge Level:1

There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?

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Which Numbers? (1)

Stage: 2 Challenge Level: Challenge Level:1

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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Alphabet Soup

Stage: 3 Challenge Level: Challenge Level:1

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

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Chameleons

Stage: 3 Challenge Level: Challenge Level:1

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

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Snail One Hundred

Stage: 1 and 2 Challenge Level: Challenge Level:1

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

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Four Coloured Lights

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

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

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Which Numbers? (2)

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

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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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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Table Patterns Go Wild!

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

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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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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Guess the Dominoes for Two

Stage: Early years, 1 and 2 Challenge Level: Challenge Level:1

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

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Guess the Dominoes

Stage: 1, 2 and 3 Challenge Level: Challenge Level:1

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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Escape from the Castle

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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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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Multiply the Addition Square

Stage: 3 Challenge Level: Challenge Level:1

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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Cinema Problem

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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Lesser Digits

Stage: 3 Challenge Level: Challenge Level:1

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

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Six Times Five

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

How many six digit numbers are there which DO NOT contain a 5?

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Numbers Numbers Everywhere!

Stage: 1 and 2

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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Triangular Triples

Stage: 3 Challenge Level: Challenge Level:1

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

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The Codabar Check

Stage: 3

This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.

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Clever Carl

Stage: 2 and 3

What would you do if your teacher asked you add all the numbers from 1 to 100? Find out how Carl Gauss responded when he was asked to do just that.

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Small Change

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

In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?

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Sept 03

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

What is the last digit of the number 1 / 5^903 ?

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Lastly - Well

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

What are the last two digits of 2^(2^2003)?

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Unlocking the Case

Stage: 2 Challenge Level: Challenge Level:1

A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?

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Unit Fractions

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

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

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See the Light

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

Work out how to light up the single light. What's the rule?

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Mini-max

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

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

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Summing Consecutive Numbers

Stage: 3 Challenge Level: Challenge Level:1

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?