I18-07

Question

The initial standing of the 16 teams coming into the football tournament is as follows: 
     Standing     Team Name       1   Team 1      2   Team 2      3   Team 3      4   Team 4      5   Team 5      6   Team 6      7   Team 7      8   Team 8      9   Team 9      10   Team 10      11   Team 11      12   Team 12      13   Team 13      14   Team 14      15   Team 15      16   Team 16      
These teams enter a football tournament where they are divided into four groups of four teams each. The format of the tournament consists of Group matches followed by Quarter Finals and Semi Finals. The winners of the Semi Finals then play for the trophy.In the Group stage, each team in a group plays against every other team in that group. A win earns the winning team 3 points, while a draw gives 1 point to each team. The losing team gets no points. The top two teams from each group advance to the Quarter Finals. In each group, all teams finished with different point totals, so there were no ties in the final group standings.
 
The position of the teams at the end of the Group stage is as given below:
      Position   Group 1   Group 2   Group 3   Group 4       1   Team 14   Team 13   Team 7   Team 9       2   Team 5   Team 12   Team 16   Team 11       3   Team 10   Team 2   Team 1   Team 3       4   Team 6   Team 8   Team 15   Team 4Format of the matches in the knockout stage is as given below:
 
 Quarter-finals: 
 
Match A: Winner of Group 1 vs Runner-up of Group 2
 
Match B: Runner-up of Group 1 vs Winner of Group 2
 
Match C: Winner of Group 3 vs Runner-up of Group 4
 
Match D: Runner-up of Group 3 vs Winner of Group 4
 
 Semi-finals: 
 
SF1: Winner of Match A vs Winner of Match D
 
SF2: Winner of Match B vs Winner of Match C
 
 Final:  Winner of SF1 vs Winner of SF2
 
In the knockout stage, there were no upsets — that is, a team with a better initial standing (as shown in the Introduction tab) always won against a team with a lower standing.

Bunuel · Answer

Official Solution:

Team 10 drew all three of its group-stage matches, so it earned 3 points.
 
Team 5 finished second in the group, so it must have had more than 3 points, and Team 14, which finished first, had more than Team 5.
 
Since both Team 14 and Team 5 drew against Team 10, Team 14 must have had 7 points (1 draw with Team 10 and 2 wins), and Team 5 must have had 4 points (1 draw with Team 10, 1 loss to Team 14, and 1 win against Team 6).
 
 Therefore, Team 5 got 4 points in the Group stage.

Correct answer:

If Team 10 drew all three of its group-stage matches, how many points did Team 5 get in the Group stage?  "4"

Bunuel · Answer

This MSR question and its solutions have been completely revised and improved.

I18-07

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Standing	Team Name
1	Team 1
2	Team 2
3	Team 3
4	Team 4
5	Team 5
6	Team 6
7	Team 7
8	Team 8
9	Team 9
10	Team 10
11	Team 11
12	Team 12
13	Team 13
14	Team 14
15	Team 15
16	Team 16