June 2003, Stage 3&4

Problems

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Racing Odds

Stage: 3 Challenge Level: Challenge Level:1

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

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Only Connect

Stage: 3 Challenge Level: Challenge Level:1

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

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Football Crazy Hockey Mad

Stage: 3 Challenge Level: Challenge Level:1

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

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Tree Tops

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

A manager of a forestry company has to decide which trees to plant. What strategy for planting and felling would you recommend to the manager in order to maximise the profit?

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In a Box

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

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

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Excel Technique: Composite Bar Charts

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

Learn how to use composite bar charts in Excel.

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Excel Interactive Resource: Fraction Multiplication

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

Use Excel to explore multiplication of fractions.

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Excel Investigation: Difference Tuples

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

Use an Excel spreadsheet to investigate differences between four numbers. Which set of start numbers give the longest run before becoming 0 0 0 0?

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Chances Are

Stage: 4 Challenge Level: Challenge Level:1

Which of these games would you play to give yourself the best possible chance of winning a prize?

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Loopy

Stage: 4 Challenge Level: Challenge Level:1

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?

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LOGO Challenge - Recollection

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

Several procedures to think about but there are several things you can do to help yourself such as breaking the procedures down stepwise (rather than into smaller peices) What does the first line do?. . . .