Conflicting Cube Counting Rules?

[auoso]

On one of the DAT Genius cube counting sections (I believe on PAT #5?), there is a cube/space that is perfectly ambiguous as to whether it could be an empty space or cube. The explanation told me the rules state that columns of cubes cannot be connected by edges and thus there must exist a cube in that position. I looked at the official rules and the only thing it stipulates is that the only cubes not shown are the ones required to support other cubes (no floating cubes). I just took the 2009 sample test and Cube figure C definitely has two columns connected by a common edge only. Does anyone know the official rule for this kind of situation?

XXX
OXX
X

Drew a picture above of what I mean. Xs are cubes, O is the ambiguous space. Last row X is connected to middle row by an edge.

Thank you!

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[molarmom]

You cannot have cubes that are connected by their edges / corners. They have to connect from one face to another face. That means that if it's not clear if a cube is present, but the figure wouldn't be fully connected by faces if the cube wasn't there, you do need to assume a cube exists to be the connecting cube. This is what I was taught as a rule, that the figure must be continuous. The 2007 and 2009 ADA exams have lots of errors in them, not just in PAT but in the sciences and QR as well.

Edit: I started to doubt myself so I just went and reread the rules. It states that the "Each figure has been made by cementing together cubes". You wouldn't be able to cement together cubes along a corner. So I'm going with that they have to bond face to face. Keep in mind that as long as the whole figure connects together face to face in some way (for example if there is another 'pathway' of cubes connecting face to face so the figure is all connected without edges bonding) then that would be legit as well

 

[KyoPhan]

Hm, I always thought it was cemented face to face. However, that problem you mention in the sample 2009 test definitely does not look like face to face.

 

[Ari Rezaei]

I also used to think the cubes had to be cemented face to face and cannot be connected by edges. However, after reviewing all the PAT rules, I can't find anything that says such a thing (even reviewing the rules posted above, all it says is the cubes have been cemented together, it doesn't specify if they were cemented together face to face or edge to edge). I think it may have been something posted by someone and just kept getting passed down. So because the ADA rules don't specify they're cemented face to face, and the 2009 test has a cube figure cemented edge to edge, I'm inclined to believe this rule is made up. They just all need to be connected somehow.

As for ambiguous cubes, where you can't tell if there is a cube there or it's just the face of another cube, I don't think the DAT would publish a question like that, I imagine many people would get the question wrong and it wouldn't be a valid measure of someone's ability, and eventually thrown out. If there was an ambiguous cube, and the entire structure is connected somehow, I would assume it would not be there, as the official rules also state 'the only hidden cubes are those required to support other cubes'. If someone could chime in if they had an ambiguous cube on their DAT that would be very helpful too.

 

[auoso]

I also used to think the cubes had to be cemented face to face and cannot be connected by edges. However, after reviewing all the PAT rules, I can't find anything that says such a thing (even reviewing the rules posted above, all it says is the cubes have been cemented together, it doesn't specify if they were cemented together face to face or edge to edge). I think it may have been something posted by someone and just kept getting passed down. So because the ADA rules don't specify they're cemented face to face, and the 2009 test has a cube figure cemented edge to edge, I'm inclined to believe this rule is made up. They just all need to be connected somehow.

As for ambiguous cubes, where you can't tell if there is a cube there or it's just the face of another cube, I don't think the DAT would publish a question like that, I imagine many people would get the question wrong and it wouldn't be a valid measure of someone's ability, and eventually thrown out. If there was an ambiguous cube, and the entire structure is connected somehow, I would assume it would not be there, as the official rules also state 'the only hidden cubes are those required to support other cubes'. If someone could chime in if they had an ambiguous cube on their DAT that would be very helpful too.

Thanks everyone for your input! I took my exam yesterday and thankfully didn't see a cube problem with this type of ambiguity. I agree with Ari that if the ADA practice test includes edge-connected columns, we can safely assume that this is fair game and not a publishing mistake. Since it is a common misconception, I feel like we should make an effort to dispel it so future test-takers aren't penalized for misguided preparation.

I've attached an actual image of the types of figures in question. Hoping this doesn't violate any kind of copyright regulation

 

[molarmom]

OK, makes sense and I'll take Ari's word.
Just to clarify for others, I guess we're assuming that the blue cubes are all connected only via the red edge to the green cube, and that they don't have to connect face-to-face, so you don't need to assume their is a cube in the ambiguous space. If this isn't a clearly outlined rule, I don't think the ADA would put something ambiguous on the test, either.

 

[Ari Rezaei]

Yeah I don't think you would get a figure that ambiguous on the real test, but in case you did, I would assume there is not a cube to the left of the green cube. The whole figure is connected by the red edge as you said.

 

[MolarDentist]

That figure looks so confusing. I've never seen anything like that. If this was ever on my test, I'll just guess.