Algorithm : Paper Folding

1. Understand the problem.
What we should be able to do, is predict the sequence of creases pointing up and pointing down for any number of foldings.
2. Device a plan.
Every time we fold the paper, we record how many creases are pointing up, or how many are pointing down. Then, we analyze the results and see if there is a sequence. If this is the case, we can stop folding the paper and proceed to make a prediction of what is going to be the result for the next number of foldings.
3. Carry out the plan.
*Place a piece of paper between your two hands, so when you first fold it the left end of the paper is on top on the right end of it.
*Unfold it, and record the direction of the crease(s).
*Repeat this step, until you notice a sequence in your observations.
4. Look back.
Using "d" for vertex pointing down, and "u" for vertex pointing up, from our recording we have:
First Folding:                        l"d"l
Second:                          l"u"l"d"l"d"l
Third:                l"u"l"u"l"d"l"d"l"u"l"d"l"d"l
 -> here we notice that the first half of the observation for the third fold is the inverted mirror image of the previous number of foldings. That is 'u' 'd' 'd' -> 'd' 'u' 'u'; the middle character is "d" because it was the result of the first fold, and it is not going to change. The second half of the recording is going to be exactly the same as the full observation of the previous number of foldings.