Direction : A number arrangement machine when given an input line of numbers…

Concept

In an input-rearrangement machine, you must first decode the single fixed rule from the worked illustration, then replay it on the new input. Read the illustration as: at every step one source number is consumed and a shorter number is pushed to the front of the line.

The governing rule here: at each step the machine takes the smallest still-unprocessed 5-digit number, keeps only its prime digits (2, 3, 5, 7) in their original left-to-right order, and places that shortened number at the front.

Why this rule (read from the illustration)

Process the original numbers in ascending order and keep only prime digits:

1. 27483 (smallest) keeps 2, 7, 3 → 273

2. 49853 keeps 5, 3 → 53

3. 57426 keeps 5, 7, 2 → 572

4. 62434 keeps 2, 3 → 23

5. 76932 keeps 7, 3, 2 → 732

6. 84629 (largest) keeps 2 → 2

Pushing each result to the front in that order reproduces Step I through Step VI of the illustration exactly, which confirms the rule.

Application to the new input

Input: 63825, 49857, 38679, 72548, 45328, 95763. Ascending order of processing: 38679 < 45328 < 49857 < 63825 < 72548 < 95763. Their prime-digit forms are 37, 532, 57, 325, 725 and 573 respectively. Inserting each at the front step by step:

1. Step I: 37 63825 49857 72548 45328 95763

2. Step II: 532 37 63825 49857 72548 95763

3. Step III: 57 532 37 63825 72548 95763

4. Step IV: 325 57 532 37 72548 95763

5. Step V: 725 325 57 532 37 95763

6. Step VI: 573 725 325 57 532 37

Result

Step VI is the last step, so the penultimate step is Step V: 725, 325, 57, 532, 37, 95763. The smallest number in that line is 37.

Cross-check

In Step V only the largest source number, 95763, is still unconverted (it is processed last, in Step VI). Among the five converted values, the two-digit ones are 57 and 37, and 37 is smaller than 57, so 37 is indeed the minimum of the line.