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Let $S[4]$ be a binary array with elements of $S$ are taken uniformly and independently from $\{0,1\}$. Also take $k$ uniformly from $\{0,1\}$. Take $i=1$. Now run the following process:

  1. Take $a,b$ uniformly and independently from $[1,4]$
  2. Change $k=(k+S[a]) \bmod 2$
  3. $S[b]=(k+S[i])\bmod 2$
  4. $i=(i+1) \bmod 4$

Run the whole process (1,2,3,4) until all elements of S are filled with 0. What is expected number of runs for this event?

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    Yes, it is similar to my previous question. However, here $i$ is deterministic. Hence, I had a doubt whether the previous approach will be applicable here or not. Yes, I am user 12290. Ok, I will submit question from my one account.2011-08-01

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