Experiment-conjecture-prove - February 2008, Stage 3&4

Problems

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Notes on a Triangle

Stage: 3 Challenge Level: Challenge Level:1

Can you describe what happens in this film?

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9 Weights

Stage: 3 Challenge Level: Challenge Level:1

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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Conway's Chequerboard Army

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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Equal Equilateral Triangles

Stage: 4 Challenge Level: Challenge Level:1

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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The Square Hole

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

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

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Road Maker

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

Which of these roads will satisfy a Munchkin builder?