Solve the numerical operations puzzle below.

If in the digit sequence “8367542741” we add 1 to the digits located at even positions and subtract 1 from the digits located at odd positions when scanning from the left, what will be the total sum of the 2nd, 4th, 7th, and 9th digits (from the left end) of the resulting sequence?

The correct answer is 16.

We are given the digit sequence: 8 3 6 7 5 4 2 7 4 1

Let us label each digit with its position (scanning from the left):

| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |----------|---|---|---|---|---|---|---|---|---|----| | Digit | 8 | 3 | 6 | 7 | 5 | 4 | 2 | 7 | 4 | 1 |

Step 1 — Apply the transformation rules:

- Even positions (2, 4, 6, 8, 10): Add 1 to the digit.
- Odd positions (1, 3, 5, 7, 9): Subtract 1 from the digit.

Working through each position:

- Position 1 (odd): 8 - 1 = 7
- Position 2 (even): 3 + 1 = 4
- Position 3 (odd): 6 - 1 = 5
- Position 4 (even): 7 + 1 = 8
- Position 5 (odd): 5 - 1 = 4
- Position 6 (even): 4 + 1 = 5
- Position 7 (odd): 2 - 1 = 1
- Position 8 (even): 7 + 1 = 8
- Position 9 (odd): 4 - 1 = 3
- Position 10 (even): 1 + 1 = 2

Step 2 — The resulting sequence is:

| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |----------|---|---|---|---|---|---|---|---|---|----| | New Digit| 7 | 4 | 5 | 8 | 4 | 5 | 1 | 8 | 3 | 2 |

Step 3 — Extract the 2nd, 4th, 7th, and 9th digits from the resulting sequence:

- 2nd digit = 4
- 4th digit = 8
- 7th digit = 1
- 9th digit = 3

Step 4 — Calculate the total sum:

4+8+1+3=16

Therefore, the total sum of the 2nd, 4th, 7th, and 9th digits of the resulting sequence is 16.