Scheme 2: Based on the average score of 10 people, the 8th, 9th and 10 people should be given to the top 7×2 = 14. Then the three of them will be less than the standard total score 14 points. The 5th, 6th and 7th places were originally 3 × 2 = 6 points more than the standard total score, but 1 × 4 = 4 should be given to the top 4. Then the three of them are 6-4 = 2 points more than the standard total score. Therefore, the sum of the scores of the 5th, 6th and 7th players is 2+ 14 = 16 points more than that of the 8th, 9th and 10 players.
Solution: Because the average score of the top seven is less than that of the top four 1 point, the average score of the top seven 10 is 2 points less than that of the top seven.
Therefore, the total score of the fifth, sixth and seventh place is three times less than the average score of the first four places, 1*7=7 points; The total score of the eighth, ninth and tenth places is 2* 10=20 points less than the average score of the first seven places, and 20+ 1*3=23 points less than the average score of the first four places.
So: the total score of the fifth, sixth and seventh places minus the total score of the eighth, ninth and tenth places = 23-7 = 16 points.
Solution: suppose the average score of the top four is a, according to the meaning of the question:
The total score of the top four is 4A, and the total score of the top seven is (A- 1)*7.
The scores of the fifth, sixth and seventh places are 7A-7-4A = 3A-7;
The total score of the top ten is (A-3)* 10,
The scores of 8, 9 and 10 are10a-30-(7a-7) = 3a-23;
Then the sum of the scores is 3A-7-(3A-23)= 16.