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Fed up with dropping questions on DAT Bootcamp's pattern folding generator, I wondered if there were some better ways to tackle one of the more common patterns: the cube. I thought, "why should I ever spend more than 30 seconds on a cube problem when it's always the same shape? Shouldn't there be a method like LoS for this?"
So I printed all the cube nets and started to experiment:
(Because hey, why not procrastinate on Destroyer problems for a little bit? 😉)
I found just a couple simple things that may help you. You probably have noticed a few of these yourself, so feel free to comment and add. This is NOT a complete method, just a few useful tips. I'll keep posting other findings as I keep practicing.
Basically I found three things:
- That spotting opposite sides is really easy (if you see opposite sides in an answer, the answer is wrong)
- A quick way to walk around the cube net and see which sides meet.
- By walking around the cube, you can also find which vertices meet, which is VERY useful for seeing if the orientation of each face is correct.
1) Eliminating Choices with Opposite sides
Here's where it gets fun: Hayang's CUBE WALKING!
2) Walking around the cube to find sides that meet
3) Using the walking method to match vertices
Summary:
- Corner sides ALWAYS touch.
- Start from a corner, then Turn-Walk or Turn-Skip to find matching sides.
- Turn-Turn gives you non-touching sides.
- Also, if you see four squares in a straight row, their farthest ends always meet. You can then use Turn-Walk/Turn-Skip in a CONVERGING direction in order to find matching sides.
- As you walk out from the corners, the vertices of the sides you encounter will join sequentially.
Conclusion
This is a rather systematic approach and will only really be useful if you get FAST at it. Right now it's best for eliminating answers based on impossible 3-side combinations and impossible contact. It's not a fully developed "method" for tackling cube folding yet, but I'll update if I find a great approach.
Meanwhile please contribute any methods you found for conquering pattern folding.
So I printed all the cube nets and started to experiment:
(Because hey, why not procrastinate on Destroyer problems for a little bit? 😉)
I found just a couple simple things that may help you. You probably have noticed a few of these yourself, so feel free to comment and add. This is NOT a complete method, just a few useful tips. I'll keep posting other findings as I keep practicing.
Basically I found three things:
- That spotting opposite sides is really easy (if you see opposite sides in an answer, the answer is wrong)
- A quick way to walk around the cube net and see which sides meet.
- By walking around the cube, you can also find which vertices meet, which is VERY useful for seeing if the orientation of each face is correct.
1) Eliminating Choices with Opposite sides
These are all of the opposites of every possible cube net.
You'll notice it's very easy to locate a side's opposite, since there are basically only two opposite-side patterns:[/SIZE]
There's another way to check if a three-side combination can exist. It goes like this:
Find the two closer sides first. Then, there are only two possibilities for the third.
For any answer choice, any valid three-side view will have two of its sides either adjacent or diagonal. Find this, and there will be only two possibilities for the third side: the non-opposites.
If the third side is an opposite, it's invalid.
If you get very fast at this elimination, it will save you time, especially on DICE problems.
However, there are problems which have repeated shapes like so:
These are the tricky ones, since you cannot eliminate invalid 3-side combinations as quickly. So perhaps a more thorough process of elimination is required. So next is a technique I noticed for finding out where one side of the cube meets with another side.[/SIZE]
You'll notice it's very easy to locate a side's opposite, since there are basically only two opposite-side patterns:[/SIZE]
- Three in a row (Cool Colors)
- Z-shapes (Warm Colors)
There's another way to check if a three-side combination can exist. It goes like this:
Find the two closer sides first. Then, there are only two possibilities for the third.
For any answer choice, any valid three-side view will have two of its sides either adjacent or diagonal. Find this, and there will be only two possibilities for the third side: the non-opposites.
If the third side is an opposite, it's invalid.
If you get very fast at this elimination, it will save you time, especially on DICE problems.
However, there are problems which have repeated shapes like so:
These are the tricky ones, since you cannot eliminate invalid 3-side combinations as quickly. So perhaps a more thorough process of elimination is required. So next is a technique I noticed for finding out where one side of the cube meets with another side.[/SIZE]
Here's where it gets fun: Hayang's CUBE WALKING!
2) Walking around the cube to find sides that meet
This technique is based on the fact that after you fold a "corner" of a cube, the sides next to the corner usually are in a position to join together as well. If you follow a few rules, you can systematically find which sides meet which by "walking outward" from a corner.
Use corners as a starting point.
Sides forming corners ALWAYS touch, and this informs us how the cube folds. From a corner, "walk" outward on both sides. You will encounter one of only three scenarios:
Turn, Walk:
One straight "walk" and one "turn" gives you two sides which meet. Fold it in your head to see how this works.
Turn, Skip:
When you encounter a corner, you SKIP it, since the two sides of the corner are NOT available for touching. After the turn-skip you again get two sides which touch.
The exception: Turn, Turn
As you walk out from a corner, if you encounter a turn-turn, the two sides do NOT touch; they turn away from each other and diverge. Start from another corner to find touching sides.
A diagram of all the matching sides in a couple of nets:
Notice how you can walk from a corner outward and use turn-walk and turn-skip to find matching sides.
Use corners as a starting point.
Sides forming corners ALWAYS touch, and this informs us how the cube folds. From a corner, "walk" outward on both sides. You will encounter one of only three scenarios:
Turn, Walk:
One straight "walk" and one "turn" gives you two sides which meet. Fold it in your head to see how this works.
Turn, Skip:
When you encounter a corner, you SKIP it, since the two sides of the corner are NOT available for touching. After the turn-skip you again get two sides which touch.
The exception: Turn, Turn
As you walk out from a corner, if you encounter a turn-turn, the two sides do NOT touch; they turn away from each other and diverge. Start from another corner to find touching sides.
A diagram of all the matching sides in a couple of nets:
Notice how you can walk from a corner outward and use turn-walk and turn-skip to find matching sides.
3) Using the walking method to match vertices
You will notice that the walking method is DIRECTIONAL. You start from a corner and you go outward. It follows then, that the pairs of vertices (the ends of each side) that you encounter as you "walk out" from a corner will meet up sequentially.
This is VERY IMPORTANT, because for each answer choice there is only one vertex (out of 8 on a cube) where the three sides can meet.
When you locate this vertex, then you can ask yourself questions like, "does this diagonal point toward or away from the vertex?" and so on. This is what will really help you.
I'll post examples soon.
This is VERY IMPORTANT, because for each answer choice there is only one vertex (out of 8 on a cube) where the three sides can meet.
When you locate this vertex, then you can ask yourself questions like, "does this diagonal point toward or away from the vertex?" and so on. This is what will really help you.
I'll post examples soon.
Summary:
- Corner sides ALWAYS touch.
- Start from a corner, then Turn-Walk or Turn-Skip to find matching sides.
- Turn-Turn gives you non-touching sides.
- Also, if you see four squares in a straight row, their farthest ends always meet. You can then use Turn-Walk/Turn-Skip in a CONVERGING direction in order to find matching sides.
- As you walk out from the corners, the vertices of the sides you encounter will join sequentially.
Conclusion
This is a rather systematic approach and will only really be useful if you get FAST at it. Right now it's best for eliminating answers based on impossible 3-side combinations and impossible contact. It's not a fully developed "method" for tackling cube folding yet, but I'll update if I find a great approach.
Meanwhile please contribute any methods you found for conquering pattern folding.
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