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: 18 62 47 93 25 70
Step I: 62 47 93 25 70 18
Step II: 62 47 93 70 25 18
Step III: 62 93 70 47 25 18
Step IV: 93 70 62 47 25 18
Step IV is the last step of this input.
Input: 38 84 16 71 29 53
Following the same rule, which number will be fourth from the left end in the last step for this input?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 38
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: 18 is the smallest of the numbers left, so it moves to the first place from the right
Step II: 25 is the smallest of the numbers left, so it moves to the second place from the right
Step III: 47 is the smallest of the numbers left, so it moves to the third place from the right
Step IV: 62 is the smallest of the numbers left, so it moves to the fourth place from the right
After Step IV the numbers stand from the largest to the smallest, so the arrangement is complete.
Apply the same rule to the input 38 84 16 71 29 53.
Step I: 16 is the smallest of the numbers left, so it moves to the first place from the right, giving 38 84 71 29 53 16
Step II: 29 is the smallest of the numbers left, so it moves to the second place from the right, giving 38 84 71 53 29 16
Step III: 38 is the smallest of the numbers left, so it moves to the third place from the right, giving 84 71 53 38 29 16
After Step III all the numbers are in their final places, so Step III is the last step.
Counting from the left end of 84 71 53 38 29 16: 84 (first), 71 (second), 53 (third), 38 (fourth).
So the number fourth from the left end is 38.