Help On 2 Cube Counting Problems

[Mycoalwin]

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Hey guys - I'm not necessarily struggling with cube counting, but some times I see certain parts of an image that confuse me whether or not a cube actually exists in that spot. I'd just like to clarify.

64) When I was doing the problem, I counted 2 cubes with only 1 side painted. One is the second to the top cube on the leftmost column; the other would be the front-most cube in the second column from the left ASSUMING there is a cube to the right of the top-left (bottom) cube. Since this is obviously wrong, how do I know when to assume a cube is there or not?

68) In the second column from the left, is there one cube at the top, followed by a gap of two cubes, and then the front-most cube which has front and back sides painted?

Mainly just looking for clarification on how to read the images. Any help would be lovely.

 

[tooth knockn]

Hey guys - I'm not necessarily struggling with cube counting, but some times I see certain parts of an image that confuse me whether or not a cube actually exists in that spot. I'd just like to clarify.

64) When I was doing the problem, I counted 2 cubes with only 1 side painted. One is the second to the top cube on the leftmost column; the other would be the front-most cube in the second column from the left ASSUMING there is a cube to the right of the top-left (bottom) cube. Since this is obviously wrong, how do I know when to assume a cube is there or not?
View attachment 184340
68) In the second column from the left, is there one cube at the top, followed by a gap of two cubes, and then the front-most cube which has front and back sides painted?

Mainly just looking for clarification on how to read the images. Any help would be lovely.View attachment 184341

For question#64- look for all the "T-boned" cubes, or a "T-section" of cubes. This includes vertical and horizontal planes of coverage on a cube..



For q#68:
Just count cubes slowly from right to left... Look carefully to which cubes are leaving 3 side open
Hope this helps

 

[jmustelier]

Hi I tried to draw out the way that I figure these out. #68 is pretty tricky.
First I always count out the number of cubes and then make a table of sides painted 0-5. This is a little time consuming at the beginning but then I race through the questions. I always end up picking up some time here because of this method.

#64 - never assume that there is a block that you can't see unless there is something on top. That being said the back bottom row would only have 2 cubes, both of 4 sides painted. The only block that I see that has 1 side painted is in the bottom left row supporting the first column.

#68 is a little bit trickier because of some crazy illusion in the back. I had to count the back bottoms cubes twice. The way I see it is that there are TWO cubes in the back right next to each. The one on the bottom left is in contact with one of the columns (3 sides painted) and the cube right next to it is only adjacent to one other cube so it has 4 sides painted. I tried to draw how the cubes are next to each other with dashed lines.

Feel free to PM me with any questions.

 

[Mycoalwin]

Hi I tried to draw out the way that I figure these out. #68 is pretty tricky.
First I always count out the number of cubes and then make a table of sides painted 0-5. This is a little time consuming at the beginning but then I race through the questions. I always end up picking up some time here because of this method.

#64 - never assume that there is a block that you can't see unless there is something on top. That being said the back bottom row would only have 2 cubes, both of 4 sides painted. The only block that I see that has 1 side painted is in the bottom left row supporting the first column.

View attachment 184351

#68 is a little bit trickier because of some crazy illusion in the back. I had to count the back bottoms cubes twice. The way I see it is that there are TWO cubes in the back right next to each. The one on the bottom left is in contact with one of the columns (3 sides painted) and the cube right next to it is only adjacent to one other cube so it has 4 sides painted. I tried to draw how the cubes are next to each other with dashed lines.


View attachment 184353
Feel free to PM me with any questions.

I use that cube counting trick too. Your response was super duper helpful, so thank you so much!