A TV station holds a math talent competition, where each participant will be scored by 8 people. The scores are F (failed), G (good), or E (exceptional). The competition is participated by three people, A, B, and C. In the competition, A and B get the same score from exactly 4 people. C states that he has differing scores with A from at least 4 people, and also differing scores with B from at least 4 people. Assuming C tells the truth, how many scoring schemes can occur?
To solve this problem, we need to determine the number of ways C can get his scores given the constraints provided. Let's break down the problem step by step.

1. **Determine the total number of scoring schemes for A and B:**
   Each participant can receive one of three scores (F, G, or E) from each of the 8 judges. Therefore, the total number of possible scoring schemes for one participant is:
   \[
   3^8
   \]
   Since A and B get the same score from exactly 4 people, we need to choose 4 out of 8 judges to give the same score to both A and B. The number of ways to choose 4 judges out of 8 is:
   \[
   \binom{8}{4}
   \]
   For the 4 judges who give the same score to A and B, there are 3 possible scores (F, G, or E). For the remaining 4 judges, A and B can each receive any of the 3 scores independently, so there are:
   \[
   3^4 \times 3^4 = 3^8
   \]
   Therefore, the total number of scoring schemes for A and B is:
   \[
   \binom{8}{4} \times 3^8
   \]

2. **Determine the number of ways C can get his scores given the constraints:**
   C must have differing scores from A in at least 4 positions and differing scores from B in at least 4 positions. We need to count the number of valid scoring schemes for C given the scores of A and B.

   Let's denote the number of positions where A and B have the same score as \( k \). Since A and B get the same score from exactly 4 people, \( k = 4 \).

   We need to consider the number of ways C can differ from A and B in at least 4 positions. We can break this down into cases based on the number of positions where C differs from both A and B.

   - **Case 1: C differs from A and B in exactly 4 positions.**
     There are \(\binom{4}{0}\) ways to choose 0 positions where C matches A and B, and \(2^4\) ways to assign scores to the remaining 4 positions. The number of ways to assign scores to the remaining 4 positions is \(3^4\).

   - **Case 2: C differs from A and B in exactly 5 positions.**
     There are \(\binom{4}{1}\) ways to choose 1 position where C matches A and B, and \(2^3\) ways to assign scores to the remaining 3 positions. The number of ways to assign scores to the remaining 3 positions is \(3^3\).

   - **Case 3: C differs from A and B in exactly 6 positions.**
     There are \(\binom{4}{2}\) ways to choose 2 positions where C matches A and B, and \(2^2\) ways to assign scores to the remaining 2 positions. The number of ways to assign scores to the remaining 2 positions is \(3^2\).

   - **Case 4: C differs from A and B in exactly 7 positions.**
     There are \(\binom{4}{3}\) ways to choose 3 positions where C matches A and B, and \(2^1\) ways to assign scores to the remaining 1 position. The number of ways to assign scores to the remaining 1 position is \(3^1\).

   - **Case 5: C differs from A and B in exactly 8 positions.**
     There are \(\binom{4}{4}\) ways to choose 4 positions where C matches A and B, and \(2^0\) ways to assign scores to the remaining 0 positions. The number of ways to assign scores to the remaining 0 positions is \(3^0\).

   Summing up all these cases, we get:
   \[
   \sum_{i=0}^{4} \binom{4}{i} \cdot 2^{4-i} \cdot 3^{4-i}
   \]

3. **Calculate the total number of valid scoring schemes for C:**
   \[
   \binom{4}{0} \cdot 2^4 \cdot 3^4 + \binom{4}{1} \cdot 2^3 \cdot 3^3 + \binom{4}{2} \cdot 2^2 \cdot 3^2 + \binom{4}{3} \cdot 2^1 \cdot 3^1 + \binom{4}{4} \cdot 2^0 \cdot 3^0
   \]
   \[
   = 1 \cdot 16 \cdot 81 + 4 \cdot 8 \cdot 27 + 6 \cdot 4 \cdot 9 + 4 \cdot 2 \cdot 3 + 1 \cdot 1 \cdot 1
   \]
   \[
   = 1296 + 864 + 216 + 24 + 1
   \]
   \[
   = 2401
   \]

Therefore, the number of ways C can get his scores given the constraints is \(2401\).

The final answer is \(\boxed{2401}\)