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: 80 shell 77 buffalo pineapple 26 44 lettuce
Step I: buffalo 80 shell 77 pineapple 26 44 lettuce
Step II: buffalo 26 80 shell 77 pineapple 44 lettuce
Step III: buffalo 26 lettuce 80 shell 77 pineapple 44
Step IV: buffalo 26 lettuce 44 80 shell 77 pineapple
Step V: buffalo 26 lettuce 44 pineapple 80 shell 77
Step VI: buffalo 26 lettuce 44 pineapple 77 80 shell
Step VII: buffalo 26 lettuce 44 pineapple 77 shell 80
Step VII is the last step of this input.
Input: 56 mustard 47 36 noodle octopus 13 fountain
Following the same rule, which of the following will be Step IV for this input?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → fountain 13 mustard 36 56 47 noodle octopus
Compare each step of the illustration with the one before it. The machine fills the line from the left end, a word and a number by turns, starting with a word. In Steps I, III, V, ... the word that comes first in dictionary order among the words not yet arranged moves to the next place from the left end; in Steps II, IV, ... the smallest of the numbers not yet arranged moves to the next place from the left end. The others keep their order.
Step I (a word): ‘buffalo’ (first in dictionary order among the words left) moves to the first place from the left
Step II (a number): 26 (the smallest number left) moves to the second place from the left
Step III (a word): ‘lettuce’ (first in dictionary order among the words left) moves to the third place from the left
Step IV (a number): 44 (the smallest number left) moves to the fourth place from the left
Step V (a word): ‘pineapple’ (first in dictionary order among the words left) moves to the fifth place from the left
Step VI (a number): 77 (the smallest number left) moves to the sixth place from the left
Step VII (a word): ‘shell’ (first in dictionary order among the words left) moves to the seventh place from the left
After Step VII every one of the words and numbers is in its final place, so the arrangement is complete.
Apply the same rule to the input 56 mustard 47 36 noodle octopus 13 fountain.
Step I (a word): ‘fountain’ (first in dictionary order among the words left) moves to the first place from the left, giving fountain 56 mustard 47 36 noodle octopus 13
Step II (a number): 13 (the smallest number left) moves to the second place from the left, giving fountain 13 56 mustard 47 36 noodle octopus
Step III (a word): ‘mustard’ (first in dictionary order among the words left) moves to the third place from the left, giving fountain 13 mustard 56 47 36 noodle octopus
Step IV (a number): 36 (the smallest number left) moves to the fourth place from the left, giving fountain 13 mustard 36 56 47 noodle octopus
So Step IV is fountain 13 mustard 36 56 47 noodle octopus.
Why the other options are incorrect
Option (2) fountain 13 mustard noodle 56 47 36 octopus — Incorrect. Here a word has been placed in Step IV, but Step IV is a number’s turn, so 36, the smallest of the numbers left, must move.
Option (3) fountain 13 mustard 36 noodle 56 47 octopus — Incorrect. This is Step V, where ‘noodle’ has also been moved.
Option (4) fountain 13 mustard 56 47 36 noodle octopus — Incorrect. This is Step III; in Step IV 36 must also move.