Logan pulled an old jigsaw box off the shelf and gazed at the picture of a carousel on the lid. Under the picture in big, bold type it stated 鈥�468 pieces鈥�.
He tipped out the contents. It didn鈥檛 look like 468 pieces. He started to count, but realised it would take a long time. What if he just counted the edge and corner pieces? That might be quicker, and if any of those pieces were missing, that would confirm that it wasn鈥檛 a complete jigsaw.
If only Logan knew how many edge pieces there were, including corners. Since there was nothing unusual about the shape of the jigsaw, how many should he expect to find?
Solution next week
#149 All in a spin
Solution
As the circumference of the plate cog is five times that of the teacup cog, most people鈥檚 first answer is that the cup will rotate five times. This isn鈥檛 correct.
The centre of each teacup rotates at a distance of 3 metres from the centre of the plate. A circle鈥檚 circumference is 蟺 脳 2r. The centre of each teacup 鈥� and also its circumference 鈥� must therefore travel 蟺 脳 6 metres to return to its starting position.
As its circumference has length 蟺 脳 1 metres, the number of teacup rotations is therefore
6蟺 梅 蟺 = 6.
Quick quiz #134
1 Which naturally occurring isotope of uranium is the most abundant?
2 What was the first UK satellite to be launched by a UK rocket?
3 Jan Jansk媒 was credited with the designation of what into four major groups?
4 Along with John Bardeen and William Shockley, who invented the point-contact transistor in 1947?
5 What is the only living species in the raptor family Sagittariidae?
Answers
1 Uranium-238
2 Prospero
3 Blood
4 Walter Brattain
5 The secretary bird (Sagittarius serpentarius)