A couple months ago I posted the following problem as a challenge to Ross Erstling to prove he has an IQ of 160:
"A certain gear system consists of 5 concentric, superposed discs: A, B, C, D and E, which are mounted on a solid platform, taken as a stationary reference. The discs have different sizes and spin at different speeds. All the discs spin at constant rates, some clockwise, some anticlockwise. Each disc has a red dot on its surface, and initially all these red dots are not lined up. At a given moment, all the discs start to spin simultaneously, each at its own speed, without any contact between them. It takes 7 minutes for disc A, 13 minutes for disc B, 17 minutes for disc C, 19 minutes for disc D and 23 minutes for disc E to complete a full 360-degree spin. After a certain time, all the red dots were aligned, disc A being in the same position that it was 2 minutes after the discs started to spin, disc B being in the same position that it was 3 minutes after the discs started to spin, disc C being in the same position that it was 4 minutes after the discs started to spin, disc D being in the same position that it was 7 minutes after the discs started to spin, and disc E being the same position that it was 9 minutes after the discs started to spin. How much time elapsed from the moment the discs started to spin until the discs reached that configuration for the first time?" Since he couldn't solve it, here is the solution by yours truly:
The problem is a tricky one, as most of the information given is irrelevant. The speed and direction of rotation of each disk is irrelevant as well as the fact that each dot is in a different position at the start of the movement, as this would only allow us to determine their relative positions in relation to one another if they had the same starting position as well as speed and turned in the same direction, clockwise or counter-clockwise. The only relevant information given are the amount of time each disk takes to turn - which absolutely makes the speed of rotation of the disks irrelevant. The fact that the time the disks take to spin is also given makes the information that some turn clockwise and others counter-clockwise irrelevant as well, since irrespective they will always be in the same position in the disk compared to the starting point! The final relevant information is that they all start spinning at the same time. We also know that at least 9 minutes have transpired since the disks started spinning, as this information is given. Taking into account all this, the solution is as follows: 9 minutes have transpired from the time the disks started spinning until the red dots on their surfaces were aligned. Explanation: since you know that at least 9 minutes have transpired since the disks started spinning, and since you can manipulate the speed and direction of rotations of the disks as you like and that they have different starting positions, you can align them whenever you want by manipulating the speed and direction of their rotation in the time alloted. This can be done to the intermediary disks, but since they all start spinning at the same moment, the size of the tiniest disk is relevant The only thing you need is to observe that the time it takes the largest disk to be at the minimum time alloted(9 minutes) coinceades with two minutes after the tiniest disk takes to complete a full 360 degree turn, which is 7 minutes. Two minutes after the smallest disks takes a full turn, it is once again at the point it was 2 minutes after it started spinning and that adds up to 9 minutes. Problem solved.
So there you have it, guys. Chalk one up for the gorilla expert! Have a pleasant day.
SUCKMYMUSCLE
