There are 81 contestants and 9 tracks. The first four contestants are required. Number of requests required

Original question from: http://topic.csdn.net/u/20120313/10/8feef8d4-6cd6-41a4-8955-a1bf7f9734b8.html

Question: We have 81 contestants and 9 tracks. We need to select the first 4. How many games are required?

First roundDivide 81 contestants into 9 groups: A, B, C, D, E, F, G, H, I

The nine components are not in the competition once and can be sorted by rank.9 games are required.

 
A B C D E F G H I1 1 1 1 1 1 1 1 12 2 2 2 2 2 2 2 23 3 3 3 3 3 3 3 3 3 3 34 4 4 4 4 4 4 45 5 5 5 5 5 5 5 56 6 6 6 6 6 6 6 6 6 67 7 7 7 7 7 7 7 78 8 8 8 8 8 8 8 8 8 89 9 9 9 9 9 9 9
 

There is no order between the group and the group, but the ranking of each group has been divided.

Second roundPlace the first place in the nine groups (A1, B1, C1, D1, E1, F1, G1, H1, i1)OnceCompetition,

Take the first four in the group where the first four are located, so that 16 contestants will be selected (the top four in the total ranking must be among the 16 contestants. Think about why ). The result is as follows:

 
A B C D 1 1 1 1 2 2 2 3 3 3 3 4 4 4 4
 

Among them, the ranking is A1, B1, C1, and D1. The ABCD group does not necessarily correspond to the ABCD group in the first round. It is only the Group of the first four winners in the second round.

Round 3After analyzing the results of the second round, we can see that the first four should be in A1, B1, C1, D1, A2, B2, C2, A3, B3, and A4 (think about why)

 
A B C D1 1 1 12 2 2x3 x X4 x
 

According to the analysis, A1 must be the first place in all rankings, and the remaining three are generated in B1, C1, D1, A2, B2, C2, A3, B3, and A4, with exactly nine contestants,One requiredThe second place is available in the competition.

So the first round of 9 games, the second round of 1 game, the third round of 1 game, a total of 11 games need to get the first four.