this month, Stage 3 & 4

August 2008

 

Problems

Why not send us your solutions?

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In the Bag

Stage:3 Challenge Level:Challenge Level:1

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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Reaction Timer

Stage:3 Challenge Level:Challenge Level:1

What are your reactions like and what affects them?

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Rotating Triangle

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

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Ishango Bone

Stage:2, 3, 4 and 5 Short Challenge Level:Challenge Level:1

Can you decode the mysterious markings on this ancient bone tool?

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Cyclic Quads

Stage:4 Challenge Level:Challenge Level:1

Points D, E and F are on the the sides of triangle ABC. Circumcircles are drawn to the triangles ADE, BEF and CFD respectively. What do you notice about these three circumcircles?

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Babylon Numbers

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

Can you make a hypothesis to explain these ancient numbers?

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Counting Fish

Stage:4 Challenge Level:Challenge Level:1

I need a figure for the fish population in a lake, how does it help to catch and mark 40 fish ?

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Snow and Cholera

Stage:4 Challenge Level:Challenge Level:1

What information helped medical pioneers decide on the cause of a disease? Especially in a time before microscopes were as powerful as they are today ?

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Olympic Magic

Stage:4 Challenge Level:Challenge Level:1

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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Lion Hunting

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

A killer lion is causing devastation. From the locations of its reported activity, can you work out where its lair is located?

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Quads

Stage:4 and 5 Challenge Level:Challenge Level:2Challenge Level:2

The circumcentres of four triangles are joined to form a quadrilateral. What do you notice about this quadrilateral as the dynamic image changes? Can you prove your conjecture?