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     Games played     Wins     Losses     Ties     Goals Made     Goals Allowed     Points  
  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     Games played     Wins     Losses     Ties     Goals Made     Goals Allowed     Points  
  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.





Correctly solved by:

1. David & Judy Dixon Bennettsville, South Carolina
2. Richard K. Johnson La Jolla, California