A word arrangement machine, when given an input line of words, rearranges them step by step following a particular rule. An illustration of an input and its rearrangement is given below.
Input: bus aeroplane cycle tram scooter rickshaw
Step I: aeroplane bus cycle tram scooter rickshaw
Step II: aeroplane rickshaw bus cycle tram scooter
Step III: aeroplane rickshaw scooter bus cycle tram
Step IV: aeroplane rickshaw scooter cycle bus tram
Step V: aeroplane rickshaw scooter cycle tram bus
Step V is the last step of this input.
Input: glue notebook ink marker chalk sharpener
Following the same rule, which of the following will be Step II for this input?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → sharpener notebook glue ink marker chalk
Compare each step of the illustration with the one before it. In each step, the longest of the words not yet arranged moves to the next place from the left end, and all the other words keep their order.
Step I: ‘aeroplane’ (9 letters) is the longest of the words left, so it moves to the first place from the left
Step II: ‘rickshaw’ (8 letters) is the longest of the words left, so it moves to the second place from the left
Step III: ‘scooter’ (7 letters) is the longest of the words left, so it moves to the third place from the left
Step IV: ‘cycle’ (5 letters) is the longest of the words left, so it moves to the fourth place from the left
Step V: ‘tram’ (4 letters) is the longest of the words left, so it moves to the fifth place from the left
After Step V the words stand from the longest to the shortest, so the arrangement is complete.
Apply the same rule to the input glue notebook ink marker chalk sharpener.
Step I: ‘sharpener’ (9 letters) is the longest of the words left, so it moves to the first place from the left, giving sharpener glue notebook ink marker chalk
Step II: ‘notebook’ (8 letters) is the longest of the words left, so it moves to the second place from the left, giving sharpener notebook glue ink marker chalk
So Step II is sharpener notebook glue ink marker chalk.
Why the other options are incorrect
Option (2) sharpener glue notebook ink marker chalk — Incorrect. This is Step I; in Step II ‘notebook’ must also move up.
Option (3) sharpener notebook marker glue ink chalk — Incorrect. This is Step III, where ‘marker’ has also been moved.
Option (4) notebook sharpener glue ink marker chalk — Incorrect. ‘sharpener’ (9 letters) is longer than ‘notebook’ (8 letters), so it must stay first.