Folding
Times
|
Up (u) or
Down (D)
|
1
|
D
|
2
|
UDD
|
3
|
UUDDUDD
|
4
|
…
|
We first did 3 experiment and tried to find the pattern. After having a guess, we, then, can make prediction based on the pattern we assumed, and compare it to the actual experiment.
Predictions
|
Actual
results
|
D
|
D
|
U D D
|
UDD
|
U U D D U D D
|
UUDDUDD
|
…
|
We found it easier to do when list the predicted result like shown in the table above. We actually thought it in a recursive way. We saw a triangle containing 4 result as a small unit of the problem.
D or U or ...
U D D U U D
Because the results in red color are always identical and in green will always be different, we can easily know all the red ones if the line above is given, and every the green one if any green one is known. Clearly, the red ones are quit simple, but the green one is harder. However, soon, we find that the two result at the right and left end of each line is always U (left) and D (right). This not only shows the problem is solvable because we can predict both all the red and green results, but it lets us to found that everything happened on one side of a line will happen adversely on the other side.
With the pattern found, we successfully predicted the fourth folding's result.
Predictions
|
D
|
U D D
|
U U D D U D D
UUDUUDDDUUDDUDD
|
We can only do the reduction from 1 to n line by line, but we cannot skip any line to do prediction and we found its really hard to write down a math expression to show our prediction. At the end of the lecture the professor indicated that we can try this in possibly. Right! After I know how to convert recursive idea into code in python I will definitely try it out!
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