Dajiang school recruitment evaluation question -- round robin problem

The author is in 2022.7 Participated in the evaluation of Dajiang .

Among them, there is a circular race problem , Record the solution ideas .

Round robin problem

Six players A, B, C, D, E, F Go round robin .

There is a competition between two players , Each player competes once a day .

Complete the round robin in five days .

It is known that ：

        The first day C Win. F,

        the second day A Win. B,

        On the third day C Lose to D,

        The fourth day A Win. F,D Lose to E

seek ： The schedule of these five days .

  Their thinking

        “ Each player competes once a day ”, Explain that within one day ABCDEF There are games , Three games in total , It's just that the opponent's combination is different . such as [AB,CD,EF] It's a situation ,[AC,BE,DF] Is another case .

        “ There is a competition between two players ”, For example, there are AB, Then there must be no AB.

        These two points , Similar to Sudoku , Every line has to have 1~9, But there can't be duplicate numbers in the same line . You can do it with Sudoku ideas .

The problem solving steps

        Title known conditions build the initial state ：(CF Express C And F The game )

        Because the fourth day already has ADEF The game of , Then the remaining game must be BC, Fill in the form ：   

        Next, let's watch the game on the third day ,CD Existing competitions , From ABEF Two matches are arranged in . because AB,AF Already exists , be A Only with E Play the game , namely AE, The remaining one is BF, Fill in the form ：

        Empathy , It is deduced that the schedule of the next day is CE,DF, The first day of the race is AD,BE：

        Not yet a pair of matches AC,BD,EF, Fill in until the fifth day , Get the final schedule ：

        Problem solving completed .