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?"
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
I believe suckmymuscle's answer is original, but also incorrect. I found his explanation rather confusing, but anyway it's pretty easy to demonstrate the problem with his answer of 9 minutes. I tried to make a graphic of this (which would make my explanation very easy to understand) but I don't know how to use my graphics software very well, so I'll just have to explain it in words. For the remainder of my explanation, I'll refer to the time that all the dots were aligned -- which is the answer to this problem -- as "the answer time."
It's true that at least 9 minutes have had to pass, since we know from the prompt that disc E traveled at for least 9 minutes before reaching alignment, at the minimum. You need only look at the behavior of any disc other than A or E to see that the answer CANNOT be 9 minutes. For the simplest example, let's look at disc D.
Here's what we know about disc D from the prompt:
1. It takes 19 minutes for disc D to complete one revolution.
2. Disc D was 7 minutes away from it's starting position at the answer time.
Clearly, given suckmymuscle's answer of 9 minutes, Disc D does not have time to complete one revolution in his solution, since 9 < 19. This shows that the dot on disc D couldn't have hit the same position twice, so suckmymuscle's answer is wrong.
To elaborate -- given suckmymuscle's answer, Disc D simply would have traveled for 9 minutes along it's path, and ended up completing about 1/2 of a revolution (9/19 of a revolution, to be exact). The prompt clearly states that, at the answer time, disc D will be 7 minutes away from the position it started at. In other words, it will have completed 7/19s, or roughly 1/3 of a revolution from its starting point. This fact is obviously incompatible with suckmymuscle's answer, as 7/19 does not equal 9/19.
If that didn't make sense, I'll try to say it even more simply. The prompt clearly tells us that disc D, at the time of the answer, will be about 1/3 of a circle away from its starting point. Suckmymuscle's answer positions disc D at about 1/2 a circle away from its starting point.
Okay, now on to my solution, which I believe is correct:
This problem really isn't that hard. We're looking for a time ("the answer time") so the answer has to be a number of minutes. How do we find it?
Well, the prompt gives us two vital pieces of information for each disc, which will help us solve the problem. The prompt tells us both HOW LONG A FULL REVOLUTION takes for each disc, and HOW FAR AWAY THE DISC IS FROM ITS STARTING POINT at the time of the answer. It's helpful to make a little table of this information (the first number is the revolution, the second number is the displacement):
A - 7, 2
B - 13, 3
C - 17, 4
D - 19, 7
E - 23, 9
So, looking at disc A, you see that a possible answer to this question is 2 minutes. After all, once two minutes have elapsed, disc A will be 2 minutes away from its starting point. The prompt tells us that when disc A is lined up with all the other dots, it will be 2 minutes away from its starting point.
So is 2 minutes the answer? Well, no, because disc B won't be in the correct position until AT LEAST 3 minutes -- the prompt also tells us this. So is three the right answer? Well no, for one thing, 3 minutes in disc A will no longer be in the same position, and Discs C-E haven't even been to the right position even once. Going on in this fashion, you will see that the first reasonable answer to test is 9 minutes.
After 9 minutes, all of the discs will have at least had the chance to get into the right position once. But this is also obviously incorrect, as we have already shown with our disc D example -- after 9 minutes, disc D will have passed the alignment position and be partially through its next revolution.
Now we need to put the final piece of the puzzle into play -- the revolution speed. See, if disc A is in the correct position after 2 minutes, it will also be in that same position at 9 minutes, 16 minutes, 23 minutes, 30 minutes and so on. This is because, as the prompt tells us, disc A completes a full revolution every seven minutes. So, if A is in the correct position after 2 minutes, then seven minutes later it will be in that same position. And seven minutes after that. And seven minutes after that, and so on to eternity.
So now we have a whole host of possible answers, 2 (we know this is wrong), 9 (we also know this is wrong), 16, 23, 30, 37, 44, 51, etc. Those are all the times that disc A will be in the correct position -- multiples of 7, plus 2.
You can do this for all the other discs. Disc B, for example, will be in the correct position after 3 minutes, 16 minutes, 29 minutes and so on (multiples of 13, plus 3).
Once you generate a huge list of all the times that each disc will be in the correct spot, all that's left is for you to find the lowest time that they all share. If there is a time when all the discs are in the correct position, then that time is when they are all aligned, and that is the answer!
This would, obviously, require you to multiply a huge amount of numbers (I started doing it by hand hoping it would, by chance, be a small number) and I would have given up right there if I didn't know a little bit about programming from college.
In the end, this simple program:
main() {
int answer = 0;
int counter = 10;
while(answer == 0) {
counter++;
if ((counter-2)%7 + (counter-3)%13 + (counter-4)%17 + (counter-7)%19 + (counter-9)%23 == 0) {
answer = counter;
}
}
printf("%i", answer);
}
when put through a C compiler, will solve the problem for you... the answer turns out to be 477,857 minutes.
Usually I don't do these sort of problems, because I'm not that great at them, but this one really was pretty easy for me. There's no way a room full of 200 MIT professors, or whatever, couldn't have solved this. I don't know anything about IQ tests, but there's no way you need an "IQ of 160+" (LOL) to solve this problem. It took me about 20-30 minutes to figure out how to solve it, and another half hour or so to remember how to code.
Hopefully my answer is easier to understand than his!
