If there are five people sitting at each table, there are four more people, and the total number of people is a multiple of five, and 1 is missing.
If there are 7 people at each table, there will be 6 more people, and the total number of people is a multiple of 7, less 1.
If there are nine people at each table, there will be eight more. The total number of people is a multiple of 9, minus 1.
Let the total number of people be n, then n = 5× 7× 9× k-1= 315k-1,where k is a natural number.
When each table is seated at 1 1 person, there are not many people, and n is a multiple of 1 1, that is, 3 15k- 1 is a multiple of 1 1.
3 15K- 1 =(308+7)K- 1 =( 1 1×28+7)K- 1 = 1 1×28K+7K- 1
So 7k- 1 is a multiple of 1 1, and k can be 8,19,30, ..., 1 1m-3, (where m is a natural number).
When k = 8, the total number of people n = 25 19.
25 19÷3=839……2
25 19÷5=503……4
25 19÷7=359……6
25 19÷9=279……8
25 19÷ 1 1=229