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All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Hidden Rectangles

Age 11 to 14
Challenge Level

 

Picture of rectangles

 

Rectangles are considered different if they vary in size or have different locations.

How many different rectangles can be drawn along the lines on a chessboard?

How many of the rectangles are squares?

What happens on an n by n board?