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Hi guys, I took the DAT last year and wanted to show you guys something that helped me on the PAT.
It has to do with dice problems. Previously, I posted a thread on solving cubes in general here:
Cube Folding: Some Findings and Tips
It will help to read the above thread first.
Now, I'll show you a systematic way to approach DICE problems, where each side has 1~6 dots.
The Method
As soon as you realize that you're looking at a dice problem, you IMMEDIATELY look at the first choice and eliminate using the following steps:
Step 1 for elimination:
- Is there a 6? If yes, is it pointing the right way?
- Are there opposites?
Step 2:
- If there is a 2 or 3, check the VERTEX where all three sides meet.
- Do 2s and 3s point TOWARD or AWAY from the vertex? Do they point the wrong way?
Step 3:
- You have a possible correct answer. (The only question left: is the CHIRALITY correct?)
- See if you can eliminate other answers QUICKLY with Steps 1/2.
Step 4:
- If you have more than one correct candidate, then you must try to visualize whether you have a correct enantiomer: Remember you fold INTO the screen. If you put these two sides together, is the last one on the top or the bottom? The left or the right?
Example Problem 1
Okay, this is a dice problem. That means IMMEDIATELY you look at the first answer, and eliminate with the following method:
Choice A:
- Is there a 6: No
- Are there opposites: YES, 2 and 4 are opposites (Z-shape) therefore WRONG.
Choice B:
- Is there a 6: No
- Are there opposites: No
- Find the vertex where all three meet: The 3 and 2 share a side, so the 1 must touch on one of the two ends of that side. To the left of this side (between 3/2), there is a corner! This means that 3 and 5 touch, so that vertex is closed.
- The vertex where 2/3 and 1 touch is on the right, and 2 and 3 are POINTING TOWARD that vertex in the net.
- BUT in choice B the 3 and 2 point AWAY from the common vertex. So this is WRONG.
Choice C:
- Is there a 6: YES.
- Does the 6 POINT THE RIGHT WAY: NO. (WRONG!)
Choice D (Correct):
- Is there a 6: YES, and it points the right way (toward the 1)
- Are there opposites: NO
- Locate the vertex where all three meet. (Use the closest corner and walk out till you reach it) The two faces AWAY from the vertex where 6 and 1 meet. This is correct.
I'll post more examples when I have time, but I hope this helps! This step-by-step method made dice problems much more efficient for me, and its principles are useful for other cube problems too.
It has to do with dice problems. Previously, I posted a thread on solving cubes in general here:
Cube Folding: Some Findings and Tips
It will help to read the above thread first.
Now, I'll show you a systematic way to approach DICE problems, where each side has 1~6 dots.
The Method
As soon as you realize that you're looking at a dice problem, you IMMEDIATELY look at the first choice and eliminate using the following steps:
Step 1 for elimination:
- Is there a 6? If yes, is it pointing the right way?
- Are there opposites?
Step 2:
- If there is a 2 or 3, check the VERTEX where all three sides meet.
- Do 2s and 3s point TOWARD or AWAY from the vertex? Do they point the wrong way?
Step 3:
- You have a possible correct answer. (The only question left: is the CHIRALITY correct?)
- See if you can eliminate other answers QUICKLY with Steps 1/2.
Step 4:
- If you have more than one correct candidate, then you must try to visualize whether you have a correct enantiomer: Remember you fold INTO the screen. If you put these two sides together, is the last one on the top or the bottom? The left or the right?
Example Problem 1
Okay, this is a dice problem. That means IMMEDIATELY you look at the first answer, and eliminate with the following method:
Choice A:
- Is there a 6: No
- Are there opposites: YES, 2 and 4 are opposites (Z-shape) therefore WRONG.
Choice B:
- Is there a 6: No
- Are there opposites: No
- Find the vertex where all three meet: The 3 and 2 share a side, so the 1 must touch on one of the two ends of that side. To the left of this side (between 3/2), there is a corner! This means that 3 and 5 touch, so that vertex is closed.
- The vertex where 2/3 and 1 touch is on the right, and 2 and 3 are POINTING TOWARD that vertex in the net.
- BUT in choice B the 3 and 2 point AWAY from the common vertex. So this is WRONG.
Choice C:
- Is there a 6: YES.
- Does the 6 POINT THE RIGHT WAY: NO. (WRONG!)
Choice D (Correct):
- Is there a 6: YES, and it points the right way (toward the 1)
- Are there opposites: NO
- Locate the vertex where all three meet. (Use the closest corner and walk out till you reach it) The two faces AWAY from the vertex where 6 and 1 meet. This is correct.
I'll post more examples when I have time, but I hope this helps! This step-by-step method made dice problems much more efficient for me, and its principles are useful for other cube problems too.
