Folding!

The reason I chose to folding problem to talk about my blog is this was the very first time I 'applied' my learnings about how to solve a problem step by step and it worked! this is a very hard problem and i was able to solve it at the end of the class!
for those of you who doesn't know what's this folding problem is:
 Take a strip of paper and stretch it so that you have one end between your left thumb and index finger and the other between your right thumb and forefinger. Fold the strip so that the left end is on top of the right end. Repeat this several times, each time folding so that the left end is on top if the right end of strip. 

Steps I took to solve this problem:

1) understand the problem [read through many times and say it with my words]

2) devise a plan :

   a) take a piece of paper and fold it as many time as you can [ I was able to fold it max 5 times]

   b) try to find a patter with [after folding it several time, I decided to make a table and write the number of times the fold is toward upward and downwards] => this step was crucial to solve this problem!!

   c) make a table : numbers & patter:

1) D

2)UDU

3)UUDUDD

4)UUDUUDDDUUDDUDD

so after this step I realized this:

                    D
                 UDU
              UUDUDD
UUDUUDDDUUDDUDD

I realized there is always a D in the middle
and it looks like a mirror, the Ds in the middle are reflecting the right hand side to the left. It's like I am taking the whole string and adding it to the right hand side of D in a new string, then negating this same string and adding on the left side of D:
 exp:
                  D
                 UDU
              UUDUDD
UUDUUDDDUUDDUDD

next step is going to be: UUDUUDDDUUDDUDD will be added to the right of D [in the middle]:

                    D
                 UDU
              UUDUDD
UUDUUDDDUUDDUDD
                    DUUDUUDDDUUDDUDD

and now I will right the exact opposite of UUDUUDDDUUDDUDD and at it to the left side of D:

                                        D
                                      UDU
                                   UUDUDD
                       UUDUUDDDUUDDUDD
UUDUUDDUUUDDUDDDUUDUUDDDUUDDUDD


ta-taaaaaa! :)