Required Mathematical Intelligence

Chapter 154 The Sentinel in the Tent
Around the tent where the leader lived, many sentries were deployed, and they lived in eight tents.At first, three sentries were required to live in each tent.Later, the Sentinels were allowed to visit each other.When the captain of the guard checks the sentries, he only counts the number of sentries in each row of tents: if there are nine sentries in each row of three tents, he thinks that he has no shortage of sentries.Seeing this, the Sentinels came up with a brilliant idea to trick their captain.One night, four sentries slipped out of the camp to have fun, without the captain of the guard noticing.The next night, six more sentries did the same without penalty.Later, the sentries even began to bring guests to the tents, inviting four at one time, eight at another, and twelve at a third.All these tricks went undetected, for nine sentries in each row of three tents were present when the captain checked.

What kind of "trick" are the sentinels looking for?

[Answer: If you want to arrange four sentries to "slip" without being discovered by the captain, you only need to meet the sum of the number of people on the four corners to be 16, and you can solve it.One way is listed here.

Similarly, if you want to arrange six sentries to "slip" without the captain noticing, you only need to satisfy that the sum of the numbers on the four corners is 18.
When four guests are invited, the sum of the number of people on the four corners is 8.
When eight guests are invited, the sum of the number of people on the four corners is 4.
Under the conditions of this question, in order not to be noticed by the captain, the number of sentries who "sneak out" cannot exceed 6, and the number of guests invited cannot exceed 12.There are many ways of arrangement, and readers who are interested can solve the problems by themselves. ]
(End of this chapter)