A number arrangement machine when given an input line of numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement:

Input: 84629 57426 76932 27483 49853 62434
Step I: 273 84629 57426 76932 49853 62434
Step II: 53 273 84629 57426 76932 62434
Step III: 572 53 273 84629 76932 62434
Step IV: 23 572 53 273 84629 76932
Step V: 732 23 572 53 273 84629
Step VI: 2 732 23 572 53 273
Step VI is the last step of the given arrangement. Based on the given logic, rearrange the given input.
Input: 63825 49857 38679 72548 45328 95763

What is the sum of all the digits of the number which is 4th smallest in step III?

The correct answer is 24.

Logic and Pattern Identification:
By analyzing the given input and rearrangement steps, we can observe two main rules applied in each step:

1. Selection Order: In each step, the smallest 5-digit number from the remaining original numbers is selected.
2. Number Transformation: Non-prime digits (0, 1, 4, 6, 8, 9) are removed from the selected number, keeping only the prime digits (2, 3, 5, 7) in their original relative order.
3. Placement: The transformed number is placed at the extreme left end of the arrangement.

Demonstration on the given example:
Original numbers sorted in ascending order:
27483 < 49853 < 57426 < 62434 < 76932 < 84629

• Step I: Pick 27483 (1st smallest) → Keep prime digits (2, 7, 3) = 273. Move 273 to the left.
• Step II: Pick 49853 (2nd smallest) → Keep prime digits (5, 3) = 53. Move 53 to the left.
• Step III: Pick 57426 (3rd smallest) → Keep prime digits (5, 7, 2) = 572. Move 572 to the left.
• Step IV: Pick 62434 (4th smallest) → Keep prime digits (2, 3) = 23. Move 23 to the left.
• Step V: Pick 76932 (5th smallest) → Keep prime digits (7, 3, 2) = 732. Move 732 to the left.
• Step VI: Pick 84629 (6th smallest) → Keep prime digits (2) = 2. Move 2 to the left.

Applying the logic to the given input:
Input: 63825 49857 38679 72548 45328 95763

Sorting original numbers in ascending order:
1. 38679 (1st smallest)
2. 45328 (2nd smallest)
3. 49857 (3rd smallest)
4. 63825 (4th smallest)
5. 72548 (5th smallest)
6. 95763 (6th smallest)

Step-by-Step Rearrangement:
• Step I: Process 38679 → Prime digits: 3, 7 → Transformed to 37.
Step I: 37 63825 49857 72548 45328 95763

• Step II: Process 45328 → Prime digits: 5, 3, 2 → Transformed to 532.
Step II: 532 37 63825 49857 72548 95763

• Step III: Process 49857 → Prime digits: 5, 7 → Transformed to 57.
Step III: 57 532 37 63825 72548 95763

Finding the 4th smallest number in Step III:
The numbers present in Step III are: 57, 532, 37, 63825, 72548, 95763.

Arranging all numbers in Step III in ascending order:
1. 37 (1st smallest)
2. 57 (2nd smallest)
3. 532 (3rd smallest)
4. 63825 (4th smallest)
5. 72548 (5th smallest)
6. 95763 (6th smallest)

The 4th smallest number in Step III is 63825.

Calculating the sum of digits:

$\text{Sum of digits}=6+3+8+2+5=24$

Thus, the sum of all the digits of the number which is 4th smallest in step III is 24.