Question

Tips about number of steps:

1. If there are $n$ words/digits in the input then at most $n-1$ steps are required to arrange it completely.

2. Number of words/digits arranged until the present step is greater than or equal to the present step number.

3. The pattern is 'number-descending-from-left and letters-ascending-from-right-alternately-pattern'.

Following the above pattern, how many steps will be required to complete the arrangement for the below given input?
goat out 34 59 set 75 peon 28

Answer 1

The rearrangement clearly happens from both directions simultaneously, but from the inside. The fact that the rearrangement is happening from the inside makes a huge difference. The numbers are arranged in ascending order from the left and the words are arranged in descending order of their appearance in the dictionary, but from the right.
Here is how you go about numbering these elements. Note that underlined elements represent those ones to the left of the L elements that you havent numbered yet. And the italicized elements represent the ones to the right of the R elements that you havent numbered yet.
$\begin{array}{ccccccccc}First:& \underset{–}{goat}& \underset{–}{out}& \underset{–}{34}& \underset{–}{59}& set& 75& peon& 28\\ & & & & & 1R& & & 1L\\ Second:& \underset{–}{got}& out& 34& 59& set& 75& peon& 28\\ & & 2R& 2L& & 1R& & 1^{\prime }R& 1L\\ Third:& \underset{–}{goat}& out& 34& 39& set& 75& peon& 28\\ & 3R& 2R& 2L& 3L& 1R& 3^{\prime }L& 1^{\prime }R& 1L\end{array}$
Now, it is easy to answer the question based on the numbering. The answer is three steps.