Cube Counting Help

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ggy

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I'm not sure how they arrived at the correct answers.

And just to clarify, there are 10 cubes total, right?
 

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I remember this one...I never could figure it out and I always chalked it up to a fluke question because technically you can't have floating (unsupported) cubes like that in cube counting anyway.
 
So even though you cannot see the "back cubes" on the second row, you still assume they are there?
 
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