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D'alar'cop and Rand al'Thor wake up and find themselves trapped in a square shaped room. Suddenly, all four walls start moving at the exact same time, and each of them moves at the same speed towards the center of the room. D'alar'cop and Rand al'Thor realize they will eventually be crushed, but they are surprised that the walls aren't colliding with each other at the edges. Explain how this is possible.

Additional details:

  • The ceiling and floor do not move.
pacoverflow
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    That would be me and my wife. "OMG, THE WALLS ARE COLLAPSING! WE'RE GOING TO DIEEEE!!!" "Yes dear, but isn't it curious that they aren't colliding with eachother? Fascina-hhhnnnngggggg-splat." – corsiKa Nov 05 '14 at 22:49
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    The trapped people part is kinda irrelevant... – Jason C Nov 06 '14 at 03:38
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    This sounds very much like the premise of the film Fermat's Room. (Spoiler warning: the article contains a poster demonstrating how the walls move) – Kevin Nov 06 '14 at 14:25
  • @LightnessRacesinOrbit It's always a square room. But the square keeps shrinking. – pacoverflow Nov 06 '14 at 14:25
  • @pacoverflow: I read "square" as "cubed" :( – Lightness Races in Orbit Nov 06 '14 at 14:37
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    Until I read "the ceiling and floor do not move" I was thinking the people were just growing, so it only seemed to them that the room was shrinking. – Steve Armstrong Nov 06 '14 at 20:38
  • @JasonC I should have worded the question better. From the perspective of the trapped people, the walls are all moving towards the center of the room. – pacoverflow Nov 06 '14 at 21:09
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    ROFL. Had to guffaw at my computer when I saw the latest edit! I was wondering if someone might do this :-) @d'alar'cop We need to work out our escape strategy... – Rand al'Thor May 19 '15 at 08:59

5 Answers5

38

The walls remain perpendicular, while moving diagonally. The left edge of each wall slides along the neighboring wall instead of colliding with it.

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eclipz905
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  • Congratulations, sir! – pacoverflow Nov 05 '14 at 21:40
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    I had literally envisioned this in my head before I realized it was the brainteaser being asked!! – corsiKa Nov 05 '14 at 22:48
  • Are these walls really "...move[ing] at the same speed [toward] the center of the room.."? – NPSF3000 Nov 06 '14 at 05:08
  • @NPSF3000 Was thinking the same thing as well, however the decrease of distance between the wall and the center of the room is the same for each wall, so I suppose one would say their speed towards the center is the same. (Just don't imagine a comma after speed) – Dennis Jaheruddin Nov 06 '14 at 09:50
  • @Dennis I'm guessing that this answer is what the OP is going for, but if you plot the movement of the walls one could argue at best it's Tangential to the center of the room. Of course, that's not the first impression someone caught in the middle of this would have... anywho good job eclipz905 – NPSF3000 Nov 06 '14 at 11:30
  • @NPSF3000 they are moving towards the center of the room... it's just not the only direction that they are moving. A vector is described by both it's "rise" and its "run", assuming a NSEW orientation, the North wall would be described by its movement South and its movement West. But you would not be wrong if you only described the Southern movement of the wall. – Jason Nov 06 '14 at 14:59
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    @Jason My answer still is not perfect. Arguably, "moving toward the center or the room" would imply that the average distance from the room's center to all points on the wall would be decreasing. Integrating to get this distance, you find that the average distance is at its minimum when each wall's sliding edge is lined up with the middle of its neighbor. After that point that average distance is increasing.

    For walls of length x, once each neighbor slides past the point x/2, you can say each wall is moving away from the center.

     – eclipz905 Nov 06 '14 at 17:30
  • @eclipz905 I suppose, though that argument ignores the fact that, to the people in the center of the room, the only points on the wall they care about are the ones not eclipsed by the other walls, and those points continue to move towards the center of the room. – Jason Nov 06 '14 at 17:59
  • @Jason You might also be able to be picky and say that while the increasing overshooting areas are part of the same structure as the walls, they're not really the walls of that room any more. Like when you talk about the walls of the room in your house, you generally consider the wall to stop at the bounds of the room regardless of where the structure goes beyond that. Just playing devil's advocate... lol. – Jason C Nov 06 '14 at 21:25
  • Speaking as a mathematician, by the "distance" from a point to a region we almost always mean the distance to the nearest point in the region, not the average distance. So for example, if I were in London I would say that I am 90 miles from France (the distance to Calais), and the distance to Nice on the far side of France is irrelevant. By that definition, the walls certainly are moving toward the centre of the room. – Steve Jessop Nov 07 '14 at 09:53
  • I made that in Minecraft! – user29530 Feb 06 '20 at 20:31
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One other idea, partially alluded to by one of warspyking's answers:

The walls are made out of a large number of very thin vertical structural members (as with a shelf of books, or a ream of paper stood on its edge). All the structural members move toward the center except for the outermost ones at each corner, which stay in place.   Decreasing book/walls illustration.

pacoverflow
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Peter K.
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  • What do you think of the "articulated wall" concept in my answer? It would have the advantage that every part of the wall would be moving toward the center; I like yours and it avoids having any part of the wall move away from center, but the outer edges aren't exactly moving "toward" the center. – supercat Nov 06 '14 at 03:30
  • @supercat Yah. That little detail bothered me a bit, since every part of my walls isn't moving inward. Your idea is better in this regard. I try to console myself with the fact that the parts the people can see are moving toward them and the parts they can't see are never moving away from them. I'm sure if they were somehow aware of these details they'd appreciate the distinction as they were being crushed. – Peter K. Nov 06 '14 at 19:13
  • I don't think the behavior of invisible parts of the wall really matters nearly as much as the fact that in the "walls move diagonally" solution the angle between the motion of the parts of walls that are near the corners versus a straight line to the center would visibly approach 90 degrees, meaning that as one approached the corners the motion would become less and less "toward the center". – supercat Nov 06 '14 at 20:55
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    This is also cool in that it could be extended to three dimensions (having the ceiling and floor move towards the center too). With its billions of parts (if each segment is to be really thin), it's totally overengineered, though. :) – zrajm Nov 07 '14 at 11:19
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Like warspyking said, the walls move through each other.

The walls are made of razor thin blades horizontally held in place with a gap the same width as the blade (separating each blade). A vertical bar that is connected at right angel to the blades is attached to one of four hydraulic motors that pushes them towards the centre. The blades could be made so thin that the wall would still look solid to the eye. If the blades were only a few atoms thick the gaps between them would also be a few atoms thick to allow the other blades from the walls at 90° to slide through but not big enough for biological molecules (including even blood cells) to fit through.

PuzzledJim
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  • Does this mean you are just making a comment on another answer? – skv Nov 06 '14 at 14:14
  • No expert on the conventions of stackexchange, but I think this deserves to be its own answer. Although warspyking's post was the inspiration for it, the earlier post gave no idea as to how the scheme could actually function. Without those details it's really not a satisfying answer. – Peter K. Nov 06 '14 at 19:17
  • From a practical matter, I don't think the walls could look solid and still have the blades slide without binding, but it would be possible to have the walls look like the top surface of a typical escalator step, with light-blocking brushes between the pieces of metal. – supercat Nov 06 '14 at 21:01
  • @supercat I think if the depth of the blades is large enough, then the walls would appear solid. – pacoverflow Nov 06 '14 at 22:00
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A limitation of the solution given by eclipz905 is that portions of the walls would be moving away from the center. An alternative approach would be to have walls of a flexible or articulated material which bend out 45 degrees at the corners. The parts of the wall which were not yet in contact with the adjoining wall would travel perpendicular to their plane toward the center, while those which had turned the corner would be moving directly toward the center at a slower rate. No part of any wall would be moving away from the center.

supercat
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    Yup. This seems like an elegant solution as well. Seen from above, your "articulated walls" would vaguely resemble lengths of bike chain with a pair of hands gradually pinching each corner together at the same rate. – Peter K. Nov 06 '14 at 19:10
0

Here's how:

The walls are made of sand (let's say), while the ceiling and floor are steel. The force on all four walls is equal, and equal at every point. Also, we are in space so there is no (or very little) gravitational force pulling the sand to the floor.

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