The year was 2006. All six teams in Pool A of World Cup hockey play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goals For- Goals Against) qualifies. In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below: Football Standings
Football Standings
Teams | Games Played | Won | Drawn | Lost | Goals For | Goals Against | Points |
---|---|---|---|---|---|---|---|
Germany | 2 | 2 | 0 | 0 | 3 | 1 | 6 |
Argentina | 2 | 2 | 0 | 0 | 1 | 5 | 6 |
Spain | 2 | 1 | 1 | 0 | 1 | 5 | 2 |
Pakistan | 2 | 1 | 0 | 1 | 0 | 2 | 3 |
New Zealand | 2 | 0 | 0 | 2 | 1 | 6 | 0 |
South Africa | 2 | 0 | 0 | 2 | 2 | 4 | 0 |
In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches:
1. Spain won both the fourth and fifth round matches.
2. Both Argentina and Germany won their fifth round matches by 3 goals to 0.
3. Pakistan won both the fourth and fifth round matches by 1 goal to 0.
When $10^{100}$ is divided by 7, the remainder is ?