A word and number arrangement machine rearranges words and numbers in a specific sequence. Given the input:

$$67 \quad hot \quad sun \quad 19 \quad best \quad 83 \quad ice \quad 49 \quad ace \quad 77 \quad cut \quad 37$$

How many steps will the machine take to complete the arrangement following the same rules as illustrated below?

**Illustration:**

Input: $$52 \quad peak \quad 91 \quad snow \quad freeze \quad 46 \quad cold \quad 15 \quad high \quad 31 \quad 73 \quad trek$$

Step I: $$15 \quad 52 \quad peak \quad snow \quad freeze \quad 46 \quad cold \quad high \quad 31 \quad 73 \quad trek \quad 91$$

Step II: $$15 \quad 31 \quad 52 \quad peak \quad snow \quad freeze \quad 46 \quad cold \quad high \quad trek \quad 73 \quad 91$$

Step III: $$15 \quad 31 \quad 46 \quad peak \quad snow \quad freeze \quad cold \quad high \quad trek \quad 52 \quad 73 \quad 91$$

Step IV: $$15 \quad 31 \quad 46 \quad cold \quad peak \quad snow \quad freeze \quad high \quad trek \quad 52 \quad 73 \quad 91$$

Step V: $$15 \quad 31 \quad 46 \quad cold \quad freeze \quad peak \quad snow \quad high \quad trek \quad 52 \quad 73 \quad 91$$

Step VI: $$15 \quad 31 \quad 46 \quad cold \quad freeze \quad high \quad peak \quad snow \quad trek \quad 52 \quad 73 \quad 91$$

Step VI is the final step of the rearrangement.

Choose the correct number of steps required to complete the arrangement for the given input.

Question

A word and number arrangement machine rearranges words and numbers in a specific sequence. Given the input:

$$67 \quad hot \quad sun \quad 19 \quad best \quad 83 \quad ice \quad 49 \quad ace \quad 77 \quad cut \quad 37$$

How many steps will the machine take to complete the arrangement following the same rules as illustrated below?

**Illustration:**

Input: $$52 \quad peak \quad 91 \quad snow \quad freeze \quad 46 \quad cold \quad 15 \quad high \quad 31 \quad 73 \quad trek$$

Step I: $$15 \quad 52 \quad peak \quad snow \quad freeze \quad 46 \quad cold \quad high \quad 31 \quad 73 \quad trek \quad 91$$

Step II: $$15 \quad 31 \quad 52 \quad peak \quad snow \quad freeze \quad 46 \quad cold \quad high \quad trek \quad 73 \quad 91$$

Step III: $$15 \quad 31 \quad 46 \quad peak \quad snow \quad freeze \quad cold \quad high \quad trek \quad 52 \quad 73 \quad 91$$

Step IV: $$15 \quad 31 \quad 46 \quad cold \quad peak \quad snow \quad freeze \quad high \quad trek \quad 52 \quad 73 \quad 91$$

Step V: $$15 \quad 31 \quad 46 \quad cold \quad freeze \quad peak \quad snow \quad high \quad trek \quad 52 \quad 73 \quad 91$$

Step VI: $$15 \quad 31 \quad 46 \quad cold \quad freeze \quad high \quad peak \quad snow \quad trek \quad 52 \quad 73 \quad 91$$

Step VI is the final step of the rearrangement.

Choose the correct number of steps required to complete the arrangement for the given input.

Accepted Answer

**Solution:**

1. **Understanding the rule:**
   - From the illustration, the machine first arranges numbers in ascending order at the beginning.
   - Then it arranges words in alphabetical order in the middle.
   - The largest numbers are placed at the end in ascending order.
   - The process is done stepwise, moving one element at a time to its correct position.

2. **Input given:**
   $$67 \quad hot \quad sun \quad 19 \quad best \quad 83 \quad ice \quad 49 \quad ace \quad 77 \quad cut \quad 37$$

3. **Separate numbers and words:**
   - Numbers: 67, 19, 83, 49, 77, 37
   - Words: hot, sun, best, ice, ace, cut

4. **Arrange numbers in ascending order:**
   - Sorted numbers: 19, 37, 49, 67, 77, 83

5. **Arrange words in alphabetical order:**
   - Sorted words: ace, best, cut, hot, ice, sun

6. **Stepwise arrangement:**
   - Step I: Move smallest number (19) to the front.
   - Step II: Move next smallest number (37) next to 19.
   - Step III: Move next smallest number (49) next.
   - Step IV: Move next smallest number (67) next.
   - Step V: Move next smallest number (77) next.
   - Step VI: Move next smallest number (83) next.

Now all numbers are arranged at the front.

- Step VII: Start arranging words alphabetically, move 'ace' next.
   - Step VIII: Move 'best' next.

The process continues until all words are arranged, but since the question asks for the number of steps to complete the arrangement, and the example shows the last step as Step VI for 6 numbers and 6 words, here with 6 numbers and 6 words, the total steps will be 8.

**Answer:** VIII

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