October 2002, All Stages

Problems

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Making Sticks

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

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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Grouping Goodies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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Multiplication Squares

Stage: 2 Challenge Level: Challenge Level:1

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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A Right Charlie

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

Can you use this information to work out Charlie's house number?

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Factor Lines

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Scoring with Dice

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

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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Divide it Out

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

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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LOGO Challenge 8 - Rhombi

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

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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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Oh for the Mathematics of Yesteryear

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

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

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Shopping Basket

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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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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Excel Technique: Using Paste Special to Lift a Copy of Values

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

Learn how to use advanced pasting techniques to create interactive spreadsheets.

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Excel Technique: Inserting an Increment Button

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

Learn how to use increment buttons and scroll bars to create interactive Excel resources.

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Excel Technique: Making a Table for a Function of Two Independent

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

Learn how to make a simple table using Excel.

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Excel Interactive Resource: Make a Copy

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

Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.

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Excel Investigation: Ring on a String

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

This investigation uses Excel to optimise a characteristic of interest.

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Diagonals for Area

Stage: 4 Challenge Level: Challenge Level:1

Prove that the area of a quadrilateral is given by half the product of the lengths of the diagonals multiplied by the sine of the angle between the diagonals.

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Number Rules - OK

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

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

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Back to Basics

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

Find b where 3723(base 10) = 123(base b).

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Flexi Quads

Stage: 5 Challenge Level: Challenge Level:1

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

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Diverging

Stage: 5 Challenge Level: Challenge Level:1

Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.

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Sine Problem

Stage: 5 Challenge Level: Challenge Level:1

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.