When a line of words and numbers is fed into a machine, the machine rearranges it step by step following a particular rule. An illustration of an input and its rearrangement is given below.
Input: sailor 60 bucket 44 train jelly 11 42 mouse 18
Step I: 60 sailor 44 train jelly 11 42 mouse 18 bucket
Step II: 60 44 sailor train 11 42 mouse 18 jelly bucket
Step III: 60 44 42 sailor train 11 18 mouse jelly bucket
Step IV: 60 44 42 18 train 11 sailor mouse jelly bucket
Step V: 60 44 42 18 11 train sailor mouse jelly bucket
Step V is the last step of this input.
Step I of another input is: 99 tortoise 55 finger 82 moth peacock 45 76 chimney
Following the same rule, which of the following will be Step III for that input?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 99 82 76 tortoise 55 peacock 45 moth finger chimney
Compare each step of the illustration with the one before it. In each step, the largest of the numbers not yet arranged moves to the next place from the left end, and the word that comes first in dictionary order among the words not yet arranged moves to the next place from the right end, both in the same step; the others keep their order.
Step I: 60 (the largest number left) moves to the first place from the left, and ‘bucket’ (first in dictionary order among the words left) moves to the first place from the right
Step II: 44 (the largest number left) moves to the second place from the left, and ‘jelly’ (first in dictionary order among the words left) moves to the second place from the right
Step III: 42 (the largest number left) moves to the third place from the left, and ‘mouse’ (first in dictionary order among the words left) moves to the third place from the right
Step IV: 18 (the largest number left) moves to the fourth place from the left, and ‘sailor’ (first in dictionary order among the words left) moves to the fourth place from the right
Step V: 11 (the largest number left) moves to the fifth place from the left, and ‘train’ (first in dictionary order among the words left) moves to the fifth place from the right
After Step V every one of the words and numbers is in its final place, so the arrangement is complete.
In Step I, 99 at the left end and ‘chimney’ at the right end are already in place. Continue from Step I with the same rule.
Step II: 82 (the largest number left) moves to the second place from the left, and ‘finger’ (first in dictionary order among the words left) moves to the second place from the right, giving 99 82 tortoise 55 moth peacock 45 76 finger chimney
Step III: 76 (the largest number left) moves to the third place from the left, and ‘moth’ (first in dictionary order among the words left) moves to the third place from the right, giving 99 82 76 tortoise 55 peacock 45 moth finger chimney
So Step III is 99 82 76 tortoise 55 peacock 45 moth finger chimney.
Why the other options are incorrect
Option (1) 99 82 tortoise 55 peacock 45 76 moth finger chimney — Incorrect. Only ‘moth’ has moved; in the same step 76, the largest of the numbers left, must go to the third place from the left.
Option (3) 99 82 tortoise 55 moth peacock 45 76 finger chimney — Incorrect. This is Step II; in Step III 76 and ‘moth’ must also move.
Option (4) 99 82 76 55 tortoise 45 peacock moth finger chimney — Incorrect. This is Step IV, where 55 and ‘peacock’ have also been moved.