Interactive Problem 1038: Group Fixtures during the Group Stage Matches of a World Cup

a)

Indicate for each of the six fixtures how many points both teams obtained (win = 3 points, draw = 1 point, defeat = 0 points).

b)

How many combinations of scores of the six games are altogether possible, i.e. in how many ways can the table be filled in?

c)

How many different possibilities exist to determine the fixtures for the three days of match?

Hint: The sequence of the games within one day and of the teams within one fixture is not being considered.

d)

Tick whether the following final tables are possible with adequate courses of games assumed.

Table I	Table II	Table III
Place Team Pts. 1st Andorra 8 2nd Botswana 5 3rd Djibouti 4 4th Cyprus 1	Place Team Pts. 1st Cyprus 6 2nd Djibouti 5 3rd Botswana 4 4th Andorra 3	Place Team Pts. 1st Djibouti 7 2nd Cyprus 4 3rd Andorra 3 4th Botswana 2

Answer:

a)

Day of match	Fixture			Points
1st	Andorra	:	Botswana	:
1st	Cyprus	:	Djibouti	:
2nd	Andorra	:	Cyprus	:
2nd	Botswana	:	Djibouti	:
3rd	Andorra	:	Djibouti	:
3rd	Botswana	:	Cyprus	:

b)
c)

d)

Table I :	not specified	possible	not possible
Table II :	not specified	possible	not possible
Table III :	not specified	possible	not possible