Even or Odd?

Write a sequence of numbers from 1 to 8192, randomly rearrange these numbers, you'll have a1,  a2,  a3,  ,  a8190,  a8191,  a8192a_1,~~a_2,~~a_3,~~\ldots,~~a_{8190},~~a_{8191},~~a_{8192} Now find the difference of every adjacent two numbers: a1a2,  a3a4,  ,  a8189a8190,  a8191a8192\vert a_1-a_2\vert,~~\vert a_3-a_4 \vert,~~ \ldots,~~\vert a_{8189}-a_{8190}\vert,~~\vert a_{8191}-a_{8192} \vert Randomly rearrange the results and you'll have a new sequence of numbers: b1,  b2,  b3,  ,  b4094,  b4095,  b4096b_1,~~b_2,~~b_3,~~\ldots,~~b_{4094},~~b_{4095},~~b_{4096} Find the difference of every adjacent two numbers: b1b2,  b3b4,  ,  b4092b4093,  b4094b4096\vert b_1-b_2\vert,~~\vert b_3-b_4 \vert,~~ \ldots,~~\vert b_{4092}-b_{4093}\vert,~~\vert b_{4094}-b_{4096} \vert Again rearrange the results and you'll have another new sequence of numbers: c1,  c2,  c3,  ,  c2046,  c2047,  c2048c_1,~~c_2,~~c_3,~~\ldots,~~c_{2046},~~c_{2047},~~c_{2048} Repeat the process above until you get a number xx. then is xx even or odd?


This is one part of 1+1 is not = to 3.
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