A word-and-number arrangement machine, when given an input line of words and numbers, rearranges it in steps. In each step two shifts happen together: the smallest odd number not already shifted is taken out and placed at the extreme left end of the line, and at the same time the largest even number not already shifted is taken out and placed at the extreme right end. If only one of the two kinds is still left, that step makes only that one shift. Every other element keeps its relative position, and the machine stops once every number has been shifted. Input: 57 dahlia 28 fennel 93 gorse 46 holly 71. Which of the following is Step 2 of the above arrangement?

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Accepted Answer

71 57 dahlia fennel 93 gorse holly 46 28. Odd numbers: 57, 93, 71. Even numbers: 28, 46. Step 1 sends the smallest odd number 57 left and the largest even number 46 right: 57 dahlia 28 fennel 93 gorse holly 71 46. Step 2 sends the next smallest odd number, 71, left and the remaining even number, 28, right: 71 57 dahlia fennel 93 gorse holly 46 28. Working from the largest odd number downwards instead would send 93 out first and leave 93 sitting second, which is the near-miss line here. Dropping each new number next to the one already placed, rather than at the extreme end, reverses both blocks.

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