A word-and-number arrangement machine rearranges a given input following a specific rule in each step. The rule involves moving the alphabetically smallest word to the leftmost side and the numerically largest number to the rightmost side in each step. The process continues until all words are arranged in alphabetical order at the left end, and all numbers in descending order at the right end.
Based on the pattern, answer the questions that follow the given input.
Input: Apple 41 Orange 62 85 Mango Banana 19
Question: What is the final (last) arrangement?

Question

Prepp Team · Accepted Answer

Arrangement Logic Explained

This question involves a specific type of rearrangement puzzle where elements (words and numbers) are moved based on defined rules in successive steps. The goal is to understand the logic and determine the state after a particular step.

Input String: $100 Orbit 35 Dream 44 67 Space Apple$

Rule: In each step, the alphabetically smallest word is moved to the leftmost available position for words, and the numerically largest number is moved to the rightmost available position for numbers. This process continues until words are alphabetically sorted at the beginning and numbers are in descending order at the end.

Step I: Initial Rearrangement

First, let's identify the words and numbers in the input string:

Words: Orbit, Dream, Space, Apple
Numbers: 100, 35, 44, 67

The alphabetically sorted list of words is: $Apple, Dream, Orbit, Space$.

The numerically sorted list of numbers (descending) is: $100, 67, 44, 35$.

Step I Actions:

Identify the alphabetically smallest word in the entire input: Apple. Move it to the first position.
Identify the numerically largest number in the entire input: 100. Move it to the last position.

Let's trace the movement:

Initial: $100 Orbit 35 Dream 44 67 Space Apple$

Move 'Apple' (the last element) to the first position:

Intermediate: $Apple 100 Orbit 35 Dream 44 67 Space$

Now, move '100' (which is now the second element) to the last position:

End of Step I: $Apple Orbit 35 Dream 44 67 Space 100$

Step II: Second Rearrangement

Now, we start Step II with the arrangement obtained from Step I:

Current Arrangement: $Apple Orbit 35 Dream 44 67 Space 100$

In this step, we focus on the elements that are not yet in their final sorted positions. 'Apple' is correctly placed at the start (position 1), and '100' is correctly placed at the end (position 8).

The remaining sequence needing rearrangement is: $Orbit 35 Dream 44 67 Space$.

Step II Actions:

Identify the alphabetically smallest word among the remaining words (Orbit, Dream, Space): This is Dream. Move it to the next available word position, which is position 2.
Identify the numerically largest number among the remaining numbers (35, 44, 67): This is 67. Move it to the next available number position, which is position 7 (just before 100).

Let's trace the movement:

Start of Step II: $Apple Orbit 35 Dream 44 67 Space 100$

Move 'Dream' from its current position (4th) to the second position. Elements to its left shift right if necessary:

Intermediate after moving Dream: $Apple Dream Orbit 35 44 67 Space 100$

Now, locate the largest remaining number, '67'. It's currently at the 6th position. It needs to move to the 7th position (the slot just before '100'). The element currently at the 7th position ('Space') needs to shift to accommodate this move, effectively moving towards the word section.

Move '67' to the 7th position:

End of Step II: $Apple Dream Orbit 35 44 Space 67 100$

This final arrangement represents the state after the second step of the rearrangement process, where 'Dream' is placed correctly as the second word and '67' is placed as the second-to-last number.