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Hoeflin's Object II.


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#1 rookie1ja

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Posted 31 March 2007 - 12:29 PM

Hoeflin's Object II. - Back to the Geometry Puzzles
The five figures shown below represent the appearance of a solid, opaque object as seen from five of its six sides. Each line shown depicts a side of the object that is perpendicular to the plane of this page. The object was constructed by gluing together a number of identical cubes so that at least one face of each added cube precisely and entirely covers and is everywhere contiguous with one face of a previous cube. Draw the sixth view of the object.
hoeflin2.gif

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
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Spoiler for Solution

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#2 Paul

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Posted 13 May 2007 - 09:02 AM

I came up with this solution:

hoeflin2-solution2.GIF[/attachment:fe3d7]

There are 12 blocks:
Assuming the first picture is the "top view",
Block positions at...
* top level: (1,2), (2,1), (2,3), (3,2) [a plus without a center]
* middle level: (1,2), (2,1), (2,2), (2,3), (3,2) [a plus with a center]
* bottom level: (1,1), (1,2), (2,1)

How can your solution have the center block at it's own level???

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#3 Some_Random

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Posted 10 July 2007 - 03:16 PM

I agree with Paul (except my answer is flipped horizontally)

I used Blender (a 3D model/render program) to make the model and I checked it from each angle and it was undeniably correct.

I also checked again and can't see a possibility where the center square could be on a third layer... it would have to be all the way at the end making the opposite view a 'plus' with a center...

So yeah, the answer is actually wrong... and now I feel like a geek.

And because I'm keen I'll add the picture
Posted Image
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#4 rookie1ja

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Posted 10 July 2007 - 04:13 PM

I might have forgotten to delete those lines in my solution ... I did this one many years ago and had the pictures drawn on a few papers with pencil (of course, with a few strikethroughs )

Edit: I have just found my old dusty paper with the drawn solution and it is indeed as you have written ... my bad
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#5 Some_Random

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Posted 11 July 2007 - 06:04 AM

No problem. It's always more fun when the answer is wrong =P
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#6 PALMEJ2

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Posted 23 August 2007 - 04:06 AM

The five figures shown below represent the appearance of a solid, opaque object as seen from five of its six sides. Each line shown depicts a side of the object that is perpendicular to the plane of this page. The object was constructed by gluing together a number of identical cubes so that at least one face of each added cube precisely and entirely covers and is everywhere contiguous with one face of a previous cube. Draw the sixth view of the object.



I'd almost argue both are correct, as based only on the five views given either solution is correct (it is impossible to determine if the center is empty or not). However, I interpret "the object was constructed by gluing together a number of identical cubes so that at least one face... is everywhere contiguous with one face of a previous cube" to mean that the cube must be a single solid body (i.e. won't fall apart). The originally posted answer with no center cube would be correct without this requirement (but would fall apart pretty easy) but is not correct with my interpretation as it is a conglomerate of 3 unconnected (at least not by an entire face) solid bodies.

See the image below. Note for the orthogonal views that the lines of the original 5 are the same. Nice catch Paul.

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#7 beerman58

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Posted 23 June 2009 - 04:19 PM

Well it looks like this solution has been entirely well-explained. But because I spent the last hour solving my own version of the solution in Excel before I read this topic, you are going to see it anyways.

Spoiler for Excel Iso View

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#8 davidh

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Posted 15 July 2010 - 03:24 PM

I solved this without any maths or engineering. If the object is a solid hexahedron then the silhouette of any side will be a mirror image of its opposite side. Thus figures 2 & 4 and 3 & 5 in the diagram are mirror images so figure 6 will be a mirror of figure 1.
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