Solving the Digit Arrangement and Sum Problem

This problem involves rearranging the digits of a given number and then finding the sum of specific digits in the new arrangement.

Step 1: Identify the Digits

The original number is 8642571. The digits present in this number are:

• 8
• 6
• 4
• 2
• 5
• 7
• 1

Step 2: Arrange Digits in Ascending Order

We need to arrange these digits from smallest to largest (ascending order). Let's list them:

The digits are: 1, 2, 4, 5, 6, 7, 8.

The new number formed by arranging these digits in ascending order is 1245678.

Step 3: Identify the Required Digits

Now, we need to find two specific digits in the new number (1245678):

• Fourth digit from the left: Counting from the left, the digits are:
  1. 1
  2. 2
  3. 4
  4. 5
  5. 6
  6. 7
  7. 8
  The fourth digit from the left is 5.
• Second digit from the right: Counting from the right, the digits are:
  1. 8
  2. 7
  3. 6
  4. 5
  5. 4
  6. 2
  7. 1
  The second digit from the right is 7.

Step 4: Calculate the Sum

The final step is to find the sum of the two identified digits (5 and 7).

Using LaTeX for the calculation:

$\text{Sum} = (\text{Fourth digit from left}) + (\text{Second digit from right})$

$\text{Sum} = 5 + 7$

$\text{Sum} = 12$

Therefore, the sum of the digit fourth from the left and the digit second from the right in the newly formed number is 12.