I saw this puzzle in some math text my girlfriend was reading the other day. A man ties a rope to each of his ankles (that is, 1 rope connecting both ankles), and then he undoes his pants, pulls them down, and, without removing them, pulls them back up inside out.
Can anyone explain how this was done? I can’t wrap my brain around it.
Couldn’t you push the pants out through the bottom of one leg of the pants?
Sounds like, if the legs were big enough, he could “pull them back up inside out”, and not be wearing the pants properly. That is, the cuffs would be near the crotch, and the waist would be near his feet.
He probably couldn’t go out in public like that, though.
The rope part is easy. It goes from one ankle up the leg, around the neck and back down the other leg. That allows you to put on and take off your pants with no problem. I don’t know how to turn the pants inside out without removing them however.
I’ve got some rope lying around.
I’ll be right back.
The missionaries at my ward showed me a trick a few weeks ago in which two people are tied together. The first person has a cord tied from his right wrist to his left wrist. The second person has a cord tied from his right wrist to his left wrist but the cord must pass through the circle formed by the other person’s body & cord. The objective is to get the people separated without breaking or untying the cords.
It seems to me that the OP’s puzzle has a similar solution to that one. Here’s the spoiler for the missionaries’ puzzle:
One person takes a bend of the other person’s cord and passes it through the loop around his own wrist. That way the people aren’t connected anymore.
I hope I got that explanation of the solution right.
Huh?
Doable, but it is kind of weaselly: it requires that the pants be large enough to fit your entire body through one of the legs. Imagine you have the rope tied as described in the OP. Your legs and the rope make a big circle:
(rope denoted by dotted line)
( )
---|---
|
-----
/ \
/__/ \__\
| |
. .
. .
. .
.....
Drop the pants and pull the legs inside out so the pants are now upside down and inside out with the legs pointing towards you, as suggested by Pygmy Rugger:
( )
---|---
|
|
[censored!]
/ \
| |
. .
. .
___ ___
\xx\ /xx/
\xxxxx/
-----
. .
...
Now you again have a pair of pants with your legs and the rope making a circle through the legs, only this time, the pants are inside out and your legs and body are “below” the pants. If you can fit through a leg hole, the entire circle (including your torso which is just a bump on this big ring) can be rotated around so you are sticking out the waist hole again.
Aha, you say: you took the pants off. However, this was just to demonstrate that the whole thing is topologically possible. If you can do this, you can also perform the inversion of the pants without actually slipping them off your legs, then when you find yourselves with the foot holes up near your thighs and the waist around your ankles, you scoot your torso and one leg in through the corresponding foot hole, stick your torso out the waist hole, and put that leg down the other leg hole.
Voila!
This ought to work:
‘Peel’ the trousers down, turning them inside out as you go; you now have them inside out and threaded on the rope. Take one end of one leg and tuck it inside itself - pull it right through and the whole garment as a tube of cloth is now still threaded on the rope, but no longer inside out. Put them back on, inverting them again as you go and you will end up wearing them inside out (and back to front, I think).
Actually, I think there might be an error in my suggestion in that peeling them off doesn’t leave them simply threaded on the rope, however, whatever state they are in when they are off your legs and on the rope, they can be turned inside out upon themselves by pushing one end inside itself and pulling it all the way through.
Snap! You can do it without having to fit through a leg. Once you get to the second picture I drew, you can turn the shorts inside out again using Askance’s suggestion (turning them inside out via one of the legholes instead of via the waist hole), which leaves you with an upside down, right-side-in pair of shorts, at which point you reverse the first step, turning them inside out again via the waist and pulling them up. I just actually did it.
Yes, I’m that curious.
Now the only thing left is doing this without actually taking them off. However, it seems obvious that this will be possible, and it doesn’t seem like a very interesting part of the problem, especially given how difficult it is to define whether or not a particular position of the pants constitutes them being “on” you once you start turning them inside out, only having one leg in them, etc.
Oops, shoulda previewed. You’re right, Mangetout, except oddly enough, they do not end up being worn backwards. If you managed to get them inside out and right side up without swapping left and right, they’d be backwards, but the process of tucking the leg inside itself swapped left and right.
Thanks for conducting the experiment; I could have done it here at work with a bit of network cable, but someone would probably walk in at the wrong moment.
Hey, it’s been, like, six hours. Shouldn’t somebody go check on Robot Arm? I have a feeling that between the rope and the pants, he may be needing some assistance.
<Upon entering the office and seeing Mangetout’s trousers entangled in network cable, the bulging eyed co-worker grapples for something to say in order to break the embarrassing tension>
Yo, Amiga, that looks pretty SCSI. Besides, your firmware’s a bit too floppy to RAM up that ASCII. Unless you want open source to format on your dongle, you better just download that gui on your Palm Pilot.
< Beet red and profusely diaphoretic, Mangetout thinks hard for a witty reply>
*Oh, Byte me. *
Well at least I tried! Given your username, I suggest you keep your attire right-side-out.
I was thinking of the technique Monty described, and I believe this is the key to the solution. Assuming the rope is tied with a somewhat loose loop around each ankle, then each trouser leg can be worked through the loop and off the foot, rotated 180 degrees, then reinstalled inside out. If this is done one leg at a time, it can be said that the pants were not removed, as the subject is always wearing at least part of them.
I don’t see how there is any possibility of getting them on inside out (and right side up, which seems to be clearly implied) without getting the feet out of the trouser legs.
Like I alluded to before, it’s possible if you only get one foot out. You can perform the “peeling down” that Mangetout describes without actually removing them from your legs, at which point you have an upside down pair of legwarmers that are attached at the bottom (inside out). Then you think of it as a tube (ignore the waist hole), and, removing one leg, you bunch the entire tube up onto the other leg. While it’s on that leg, it can be turned inside out end-through-end. Then you reverse the rest of the process: unbunch it so it covers both legs like legwarmers (only this time it’s right-side-in, and then do the “peeling down” backwards so you’re wearing a regular inside out pair of pants.
BTW, my hat is off to anyone who was able to come up with this without actually experimenting with a physical pair of pants. It’s all very clear to me now, but there is no way my brain was going to believe it without some hard evidence.
Well, if his pants were inside out to begin with, pulling them down and immediately pulling them back up wouldn’t change their status.
I’m pretty sure this is the answer: