A number arrangement machine, when given an input line of numbers, rearranges them step by step following a particular rule. An illustration of an input and its rearrangement is given below.
Input: 34 71 19 56 42 88
Step I: 34 71 56 42 88 19
Step II: 71 56 42 88 34 19
Step III: 71 56 88 42 34 19
Step IV: 71 88 56 42 34 19
Step V: 88 71 56 42 34 19
Step V is the last step of this input.
Input: 47 85 26 63 38 91
Following the same rule, which of the following will be Step III for this input?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 85 63 91 47 38 26
Compare each step of the illustration with the one before it. In each step, the smallest of the numbers not yet arranged moves to the next place from the right end, and all the other numbers keep their order.
Step I: 19 is the smallest of the numbers left, so it moves to the first place from the right
Step II: 34 is the smallest of the numbers left, so it moves to the second place from the right
Step III: 42 is the smallest of the numbers left, so it moves to the third place from the right
Step IV: 56 is the smallest of the numbers left, so it moves to the fourth place from the right
Step V: 71 is the smallest of the numbers left, so it moves to the fifth place from the right
After Step V the numbers stand from the largest to the smallest, so the arrangement is complete.
Apply the same rule to the input 47 85 26 63 38 91.
Step I: 26 is the smallest of the numbers left, so it moves to the first place from the right, giving 47 85 63 38 91 26
Step II: 38 is the smallest of the numbers left, so it moves to the second place from the right, giving 47 85 63 91 38 26
Step III: 47 is the smallest of the numbers left, so it moves to the third place from the right, giving 85 63 91 47 38 26
So Step III is 85 63 91 47 38 26.
Why the other options are incorrect
Option (1) 47 85 63 91 38 26 — Incorrect. This is Step II; in Step III 47 must also move to the third place from the right.
Option (2) 85 91 63 47 38 26 — Incorrect. This is Step IV, where 63 has also been moved.
Option (4) 91 85 63 47 38 26 — Incorrect. This is the last step (Step V), with all the numbers in place.