Get it in Gear (Posted on 2003-08-15)

	Submitted by Bryan
Rating: 4.3333 (3 votes)
Solution:	(Hide)
As two gears turn, the same number of teeth on each gear will pass through the point where they mesh, regardless of the number of teeth on each gear. For example if gear A is turned such that 5 teeth pass through the point where A and B mesh, then 5 teeth on gear B will pass through that point as well. At the same time, 5 teeth on gear B will pass through the point where B and C mesh, or in other words, all gears will rotate by 5 teeth if one does. Therefore, if all the gears rotate such that the lowest common multiple of the number of gear teeth pass through a given point, all the gears will rotate an integral number of times, and their stripes will all be vertical again. If that number is cut in half, some of the gears will still rotate an integral number of times, and others will make several full revolutions and one half revolution, and all the lines will still be vertical. The LCM of teeth for the four gears is 2²*3³*5*7*17. If gear A (which has 5*7 teeth) rotates until this many teeth pass a given point, it will make 2²*3³*17 revolutions. Half this number is 2*3³*17 or 918 revolutions.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-04-27 23:52:50
	re: Simple LCM	Lawrence	2003-08-24 06:09:18
	Simple LCM	Lawrence	2003-08-24 05:59:40
	No Subject	Dave Cheetham	2003-08-17 12:21:44
	A correction	Federico Kereki	2003-08-15 22:13:09
	re: The Mechanical Revolution	Charlie	2003-08-15 14:49:10
	re: The Mechanical Revolution	Bryan	2003-08-15 14:28:59
	The Mechanical Revolution	Gamer	2003-08-15 14:18:10