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A word-and-number arrangement machine rearranges any input line in steps, alternating between two shifts. In every odd-numbered step (Step 1, 3, 5, ...) the smallest number that has not already been shifted in an earlier step is taken out and placed at the extreme right end of the line. In every even-numbered step (Step 2, 4, 6, ...) the word that comes last in alphabetical order among the words not already shifted in an earlier step is taken out and placed at the extreme left end of the line. All the remaining elements keep their relative order, and the machine stops when no further shift is possible.
Input: 57 92 axe beam 16 coal 63 drum.
How many steps are needed to complete the rearrangement of the above input?

Competition practiceInput-Output
  • A9
  • B7
  • C8
  • D10

Step-by-Step Solution

Each step fixes one element that the rule targets, and the last step is Step 8: axe beam coal drum 16 57 63 92. No further shift is possible after that, so 8 steps are needed.
Answer: C) 8

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