Hockey Standings are based on points:
Each win is 2 points,
Each loss is 0 points,
Each tie is 1 point.
In this league, each team plays each other once.
Fill in the missing numbers in the standings:
| Team
|
Gam
played
|
W
|
L
|
T
|
Goals
Made
|
Goals
Allow
|
Pts
|
| A
|
4
|
|
|
|
7
|
1
|
5
|
| E
|
2
|
|
|
|
2
|
6
|
0
|
| D
|
4
|
|
|
|
5
|
|
3
|
| C
|
3
|
|
0
|
|
|
4
|
3
|
| B
|
|
|
|
|
5
|
2
|
|
Solution to the Problem:
| Team
|
Gam
played
|
W
|
L
|
T
|
Goals
Made
|
Goals
Allow
|
Pts
|
| A
|
4
|
2
|
1
|
1
|
7
|
1
|
5
|
| E
|
2
|
0
|
2
|
0
|
2
|
6
|
0
|
| D
|
4
|
1
|
2
|
1
|
5
|
10
|
3
|
| C
|
3
|
0
|
0
|
3
|
4
|
4
|
3
|
| B
|
3
|
2
|
0
|
1
|
5
|
2
|
5
|
First, recognize that if one game is played, it shows up as two games in the standings because two teams were involved. Also,
a total of two points will show up in the standings (either a tie in which both teams get one point; or a win and a loss, in which
one team gets 2 points and the other none).
Since E has no points, it must have lost both of its games.
So, you can fill in 0 - 2 - 0 for its record.
Since C has 3 points, and 3 games and no losses, it must have 3 ties and no wins. So, you can fill in its record.
Also, since all of its games were tied, they must have scored 4 goals. Since the total goals scored must
equal the total goals allowed, team D must have allowed 10 goals.
For team B, games played must have been 1 or 3, since the total of games played must be even, and the most games that a
team could play would be 4 (if they have played each of the other teams once). If they had played 1 game,
their ppoints would be 3 (the total of the games would be 14 which means the total points would be 14), but that is impossible.
Therefore, team B must have played 3 games for a total of 5 points (since 16 games played means 16 points). So,
team B won 2, lost 0, and tied 1 (to get 5 points).
Since the total of teams E, C, and B is 2 wins, 2 losses, and 4 ties, the records of teams A and D must have the same
number of wins as losses and an even number of ties. So, there are only two possibilities:
| Team
|
Won
|
Lost
|
Tie
|
| A
|
1
|
0
|
3
|
| D
|
0
|
1
|
3
|
or
| Team
|
Won
|
Lost
|
Tie
|
| A
|
2
|
1
|
1
|
| D
|
1
|
2
|
1
|
But possibility #1 is impossible because Team A would have had to beat a team by 6 goals
(if they only won one game), but no other team could have lost a game by 6 goals.