bonanova Posted October 6, 2008 Report Share Posted October 6, 2008 Can a cube be passed through a hole in a smaller cube? Quote Link to comment Share on other sites More sharing options...
0 Yoruichi-san Posted October 6, 2008 Report Share Posted October 6, 2008 many dimensions are we allowed? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 many dimensions are we allowed? * takes a quick glance at the puzzle title, hoping no one notices, and then confidently replies * Three. Quote Link to comment Share on other sites More sharing options...
0 Prime Posted October 6, 2008 Report Share Posted October 6, 2008 Yes, if... The larger cube is a sponge, and/or smaller is made of some stretcheable elastic material. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 Sure If Chuck Norris wants it to. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 * takes a quick glance at the puzzle title, hoping no one notices, and then confidently replies * Three. I think it is possible if the smaller cube is just slightly smaller than the bigger one, and the hole is from 1 corner drill through to the opposite corner (in 3 D manner), with the diameter of the edge of the bigger cube. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 Can a cube be passed through a hole in a smaller cube? Only if it was made of softer material Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 I think it is possible if the smaller cube is just slightly smaller than the bigger one, and the hole is from 1 corner drill through to the opposite corner (in 3 D manner), with the diameter of the edge of the bigger cube. Hi woon, I don't know how to discuss your answer without spoiling the puzzle, so ... let me promise to give you a reason later but say for now your solution won't work. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 No stretching or compressing, guys ... sheesh!!! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 (edited) Was thinking if ... When, for example, the Length of a side of the smaller cube is x and name this cube A. The Length of a side of the larger cube is x+1 and name this cube B. You drill a hole into A into face FA in such a manner that the four corners of FA lies on the circumference of the circle. This will make the each side of FA a chord in the circle and the diameter of a circle is the longest chord in that circle, a larger size cube should be able to go through it. => Hope it is confusing enough. j/k. Let's see what some people have to say about this BS EDIT: Typo Edited October 6, 2008 by Ben Law Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 Was thinking if ... When, for example, the Length of a side of the smaller cube is x and name this cube A. The Length of a side of the larger cube is x+1 and name this cube B. You drill a hole into A into face FA in such a manner that the four corners of FA lies on the circumference of the circle. This will make the each side of FA a chord in the circle and the diameter of a circle is the longest chord in that circle, a larger size cube should be able to go through it. => Hope it is confusing enough. j/k. Let's see what some people have to say about this BS EDIT: Typo So ... would that be possible? Equivalent approach: Think of the cubes as equal in size. See if that problem is solvable, and if so, is there any extra clearance? If so, then the one with the hole can be shrunk very slightly and preserve the solution. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 I think Woon has it, but here's a diagram to make it clearer: Looked at corner-on, a 1cm cube is equivalent to a hexagon of side ((2/3)^0.5)cm (I think) You can just about squeeze a 1cm square into that, so a slightly larger cube would also go Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 I make the limit to be... sqrt(8)/(sqrt(3)+1) = approx 1.035 (ratio of cube sizes) Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 I think Woon has it, but here's a diagram to make it clearer: Looked at corner-on, a 1cm cube is equivalent to a hexagon of side ((2/3)^0.5)cm (I think) You can just about squeeze a 1cm square into that, so a slightly larger cube would also go Exactly. he implied a circular hole would be drilled. It turns out that the inserted cube's face diagonal would have to be the diameter of that drilled hole, and that is exactly the diameter of the inscribed circle of the hexagonal cross section that optimally provides room for the cube to pass, given that it has a preferred angular position. I have a drawing - like yours - that shows the inscribed circle. The upshot is that for equal size cubes, it passes through, but with zero clearance and 0-thickness walls at some points. Therefore the cube with the hold could not be shrunk to satisfy the puzzle. If Woon had not used a circular hole, his answer would have been correct. So ... woon ... if you're reading ... that's why. -bn Quote Link to comment Share on other sites More sharing options...
0 Yoruichi-san Posted October 6, 2008 Report Share Posted October 6, 2008 Exactly. he implied a circular hole would be drilled. It turns out that the inserted cube's face diagonal would have to be the diameter of that drilled hole, and that is exactly the diameter of the inscribed circle of the hexagonal cross section that optimally provides room for the cube to pass, given that it has a preferred angular position. I have a drawing - like yours - that shows the inscribed circle. The upshot is that for equal size cubes, it passes through, but with zero clearance and 0-thickness walls at some points. Therefore the cube with the hold could not be shrunk to satisfy the puzzle. If Woon had not used a circular hole, his answer would have been correct. So ... woon ... if you're reading ... that's why. -bn Nice. To give Woon credit, though, I think he didn't mean a circular hole, it's just that English is not his first language...;P Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 If you can see the green circle, what you have is three figures, looking along body diagonal of the cube with a hole[black hexagon] one of the cube axes [red] of the other cube, and the inscribed circle [green] of the hexagon, for which the red figure is the inscribed square. If a circular hole is drilled along the cube diagonal, a red cube of the same size as the black cube passes through, with zero clearance. Also, the walls of the black cube have zero thickness at six points. So you can't drill a circular hole and use it to pass a cube through a smaller cube. But if you create a square hole slightly larger than the red cube face, it will clear the black cube walls and permit the red cube to pass, even if you shrink the black cube ever so slightly. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 Nice. To give Woon credit, though, I think he didn't mean a circular hole, it's just that English is not his first language...;P Fair enough. We have co-solvers, and I'll edit the puzzle tag line to so indicate. Good job all! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 Exactly. he implied a circular hole would be drilled. It turns out that the inserted cube's face diagonal would have to be the diameter of that drilled hole, and that is exactly the diameter of the inscribed circle of the hexagonal cross section that optimally provides room for the cube to pass, given that it has a preferred angular position. I have a drawing - like yours - that shows the inscribed circle. The upshot is that for equal size cubes, it passes through, but with zero clearance and 0-thickness walls at some points. Therefore the cube with the hold could not be shrunk to satisfy the puzzle. If Woon had not used a circular hole, his answer would have been correct. So ... woon ... if you're reading ... that's why. -bn I knew what you mean now! While others are mislook on the 3 D I keep thinking hole must be circular! The hole should be as the 2-D shape of the bigger cube, that's it. Right? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 6, 2008 Author Report Share Posted October 6, 2008 I knew what you mean now! While others are mislook on the 3 D I keep thinking hole must be circular! The hole should be as the 2-D shape of the bigger cube, that's it. Right? Yup. Nice job! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 Yup. Nice job! Thanks. This is a nice one. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 *Sulking* I still think Chuck would have done a better job though. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 6, 2008 Report Share Posted October 6, 2008 I knew what you mean now! While others are mislook on the 3 D Well Done and Hi5 to you my friend Diagonals - I will remember it Quote Link to comment Share on other sites More sharing options...
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bonanova
Can a cube be passed through a hole in a smaller cube?
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