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: 49 96 50 64 41 63
Step I: 50 49 96 64 41 63
Step II: 50 41 49 96 64 63
Step III: 50 41 63 49 96 64
Step IV: 50 41 63 64 49 96
Step V: 50 41 63 64 96 49
Step V is the last step of this input.
Input: 66 57 60 98 72 74
Following the same rule, which number will be second from the left end in the last step for this input?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 72
Compare each step of the illustration with the one before it. In each step, the number with the smallest unit digit (last digit), among the numbers not yet arranged, moves to the next place from the left end, and all the other numbers keep their order.
Step I: 50 has unit digit 0, the smallest among the numbers left, so it moves to the first place from the left
Step II: 41 has unit digit 1, the smallest among the numbers left, so it moves to the second place from the left
Step III: 63 has unit digit 3, the smallest among the numbers left, so it moves to the third place from the left
Step IV: 64 has unit digit 4, the smallest among the numbers left, so it moves to the fourth place from the left
Step V: 96 has unit digit 6, the smallest among the numbers left, so it moves to the fifth place from the left
After Step V the numbers stand in increasing order of their unit digits, so the arrangement is complete.
Apply the same rule to the input 66 57 60 98 72 74.
Step I: 60 has unit digit 0, the smallest among the numbers left, so it moves to the first place from the left, giving 60 66 57 98 72 74
Step II: 72 has unit digit 2, the smallest among the numbers left, so it moves to the second place from the left, giving 60 72 66 57 98 74
Step III: 74 has unit digit 4, the smallest among the numbers left, so it moves to the third place from the left, giving 60 72 74 66 57 98
After Step III all the numbers are in their final places, so this is the last step.
Counting from the left end of 60 72 74 66 57 98: 60 (first), 72 (second).
So the number second from the left end is 72.