# Given five drawn shapes in a sequence, infer the next shape...?

Several.

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#### mmm4444bot

##### Super Moderator
Staff member
Several identical cubes are fused to form a solid object. Given the following five views of such an object, draw the sixth.

Look for a pattern, reading from left to right. What has happened to the first shape, to create the second?

#### lev888

##### Junior Member
Look for a pattern, reading from left to right. What has happened to the first shape, to create the second?
I think these are 5 projections of a 3D object along one of the axes, and we need to draw the last one.

#### lev888

##### Junior Member
Yes, this somehow is supposed to make a 3-D object. Do we know what the object will look like once constructed?
That's what you need to figure out to determine what the last projection is. I would start with grouping the views into pairs (2 directions for each axis).

#### lev888

##### Junior Member
I get that the second and third are related and the fourth and fifth are related. So, I'm guessing the sixth, unknown shape will resemble the first shape somehow. i'm just not certain exactly how it will look.
I agree. Although there's something not quite right with 4 and 5.
If you see a rectangle that's 2 "fused" cubes. If there is a line in the middle, there is another cube in front.

#### mmm4444bot

##### Super Moderator
Staff member
Whoops -- I had jumped directly from the subject line to the image, so I missed the six cubes.

These are side/top/bottom views of an object constructed by joining six identical cubes together. Also, I suspect that the five given views are not necessarily oriented in any way.

I think that a rectangle signifies two adjacent cubes located the same distance from the viewer. In other words, the faces of these two cubes form a rectangle because each face lies in the same plane. (There could be another cube behind the rectangle, in a view.) But a square next to a rectangle indicates that the face we see as the square lies at a different distance (closer or farther) than the cubes forming the rectangle.

Looking at #5, there are three cubes whose faces are at the same distance, and there are two other cubes whose faces are at a different distance. Where is the sixth cube? I think I can imagine its position, to render the other given viewpoints.

If I'm correct, the missing view will look like an L-shape, with a square attached to one of its longer sides.

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#### lev888

##### Junior Member
The use of the word "cubes" in the question is kinda throwing me off. A cube by definition is symmetrical and comprised of six equal squares and it's hard to see how the given pieces smoothly form "identical cubes" to be fused into some larger "object," whatever shape that might take.
The given pieces? You mean the 5 views? Those are 5 views of a single piece/object, which is formed by fusing several small cubes.

Take 2 cubes, put them on the floor side by side and look down. Imagine they fit together perfectly and there is no line in the middle. What shape do you see? A rectangle. Now add another "above" the left cube. You get an "L". Now put another cube on top of the one in the middle. The shape is still an "L", but now you see 2 lines - the edges of the last added cube.
The problem gives you 5 views of the object (for example: top, bottom, left, right, front) and asks you to deduce what it looks like from the back.
Hope it's clearer.

#### mmm4444bot

##### Super Moderator
Staff member
How is it possible to deduce the shape of the object without knowing what the object is to begin with?
You can deduce the shape of the object, by analyzing the given views. This requires some spacial aptitude. To help, I made sketches, starting with possibilities from image #5.