13th man optical illusion response

observations

1.  There are 24 body parts in all - 12 on top and 12 below
2.  In 12-man picture 2 parts each combine to form 12 men
3.  In 13-man picture 2 parts pair in 11 places - while 1 top part and 1 lower part dont pair - forming 13 men

question: how is the 13th man formed?
assumption: the resultant men in 12-man picture are full men

4.  The heights of all men in 12-man picture are the same
5.  The heights of all men in 13-man picture are the same
6.  The height of each man in 13-man picture is 11/12th that of each man in 12-man picture
7.  That is somehow, each man in 12-man picture contributes 1/12th of himself to create the 13th man
8.  Hence, everyone is in on it!! (digress - ever saw ShawShank Redemption?)

how to visualize the problem and solution

9.  Each of the 24 part has two characteristics: i. its size  ii. its position
10. We can transform the picture(s) to understand this better
   i.   arrange the top parts in ascending order
   ii.  arrange the lower parts in ascending order
   iii. number them (t1, t2,....l1, l2)
                            (tx,..lx..)
                    t1 means (1) 't'op part  (2) '1'st part  (3) size '1'/12
                    tx means (1) 't'op part  (2) 'x'th part  (3) size 'x'/12

   iv.  for 13-man picture, tx    lx    11
                                      -- + -- = --
                                      12   12   12

   v.   paint them - I havent figured how to do this but I seem to believe 2 colours used smartly could help



other observations

11. In the 12-man picture, we can group them in 5 rows:

     row1 = 3 men, row2 = 2 men, row3 = 2 men, row4 = 3 men, row5 = 2 men

     and in the 13-man picture, we have:

     row1 = 3 men, row3 = 2 men, row3 = 2 men, row4 = 3 men, row5 = 2 men

i.e picture 1: 32232

   picture 2: 33232

so we can say that the extra man is the 3rd man on row 2. he happens to be the man who looses in feet when moving from 1 to 2.

12. Ok, it is difficult to notice how the 13th man forms so let's concentrate on a part of the picture - the heads.  Let's see how the 13th head is formed.  Let's concentrate on the middle line.  In 12-man picture, there are 4 heads on the middle line, in 13-man picture, there are 5!!.  So, the 13th head appears on the middle line.

outstanding questions

1.  To explain the phenomenon in a more succint, straightforward, understandable manner
2.  Who developed the illusion?

why is this explanation so long??

Take this as a mathematical problem that is still being solved, 'a' solution is not complete yet.  When it is, it 'will' be presented in a more succint manner.  Also, note that the developer of the problem would have spent time and space in creating this problem.  Therefore, it is logical that it takes a commensurate amount of effort to solve the problem too

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http://www.laurenceholbrook.com/Misc/rxtramanGIF_Explanation.html