Answer to Riddle #84: Twiddled Bolts
An unusual puzzle this because your ability to answer depends on not your pure intelligence but your ability to visualize things in the abstract. It's also not the slightest bit quant. I read this puzzle the other day, and I've been thinking of a way to explain it, I think I've come up with a good plan, let's see if you agree:
Consider the arrangement below:
It shows rather than two interlocking bolts, one bolt and a sort of specially designed thing with a singular thread in a circle around it.
It's reasonably easy to tell by intuition that given the orbital direction that the stud at the top (currently,) will move to the right.
Now consider the arrangement below...
The stud will also move to the right.
So if both are moving to the right, at the same speed, then there is no relative motion, (save the rotation,) at all.
Finally as the convincer I've included a video...
To see the video you'll have to click here. The video will appear below, or to view it in YouTube you can click click here. Apologies for this nonsense, it's because you're on a mobile device and Google thinks this page is not mobile friendly if I embed YouTube videos using their own code.
I know, I know, I twiddled the bolts in the opposite direction. Hopefully you can see that if the don't move relative to each other when twiddled one way they wont when twiddled the other.
Puzzle comes from a book, My Best Mathematical Puzzles by Martin Gardner
I couldn't help but think Bard may have cheated on this one...
If you're curious what Bard made of this puzzle...
When you twiddle the bolts, you are essentially moving them in a helical path. The distance between the heads of the bolts will remain the same because the helical paths of the bolts are identical.
Here is a diagram to help you visualize it:
[Image of two bolts with helical grooves intermeshing. The bolts are being twiddled in the direction shown. The distance between the heads of the bolts remains the same.]
If you're curious what ChatGPT made of this puzzle...
When two identical bolts are placed together so that their helical grooves intermesh, they form a screw thread. Twiddling the bolts in the direction shown will cause the screw thread to move downwards (or upwards, depending on the orientation), and the distance between the heads of the bolts will remain the same.
The reason for this is that the screw thread is designed so that when it is rotated, it moves along its own axis (i.e., it either moves up or down), but it does not move sideways. Therefore, as the screw thread moves downwards, the bolts will not move inward or outward, but they will maintain the same distance from each other.
So the answer is:
The heads will stay the same distance apart from each other.
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