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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.
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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?
Age 11 to 14
Challenge Level
Imagine that you are sitting in a room at ground level, facing a floor-to-ceiling window which is 20 feet by 20 feet.
A huge concrete wheel, 100 miles in diameter, is rolling down the street and is about to pass right in front of the window, from left to right.
The centre of the wheel is moving to the right at 100 miles per hour.
What does the view look like, from inside the room, as the wheel passes by?
This problem appears in "Mathematical Thinking and Problem Solving", edited by Alan Schoenfeld and published by LEA press.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.