The problem is essentially asking for a number that must have been skipped when summing the first few natural numbers resulting in a total of 177. The formula for the sum of the first `n` natural numbers is n*(n+1)/2. The value closest to 177 using this formula comes at n=19, yielding 190. Hence, we subtract 177 from 190, which equals to 13. So, the candidate must have missed the number 13 when adding them up. Looking at the options:

Option 1: 11 - If the missed number was 11, the sum would have been 179, which is not the case.

Option 2: 12 - If the missed number was 12, the sum would have been 178, which isn`t our target number.

Option 3: 13 - As explained above, if the missed number was 13, the sum would be 177 which is our target number.

Option 4: 14 - If the missed number was 14, the sum would have been 176, which isn`t the required total.

Hence, The correct answer is option 3.