Answer to September 28, 1998 Problem |
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Soccer Stumper Proposed by David L. Book, in The Washington Post.In the first round of this year's World Cup, the teams in Group G finished as follows: TEAM GF GA Points ---------- ---- ---- ------ Romania 4 2 7 England 5 2 6 Colombia 1 3 3 Tunisia 1 4 1GF stands for "Goals For" and GA stands for "Goals Against." A victory earns three points and a tie one; a loss earns no points. Each team played the other three once. What were the scores of all the matches? NO fair looking them up!! |
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Solution to Problem:
The only way to total 7 points is by having 2
wins and a tie; the only way to total 6 points
is by having 2 wins and a loss; etc; so it is
easy to determine the outcome of each match.
Since all matches in this group involved little
scoring, the fastest way to determine the
number of goals is by trial and error. But if
you want to do it mathematically, you can
construct a 4 x 4 matrix and solve for the 12
unknowns:
Rom Eng Col Tun Rom - A B C 4 Eng D - E F 5 Col G H - I 1 Tun J K L - 1 2 2 3 4Romania defeated England, 2-1. Romania defeated Colombia 1-0. Romania tied Tunisia, 1-1. England defeated Colombia, 2-0. England defeated Tunisia, 2-0. Colombia defeated Tunisia, 1-0. |
1. Kaveh Sadeghzadeh | Williamsburg, VA |
2. Barrett Waybright | Winchester, VA |
3. Darren Rennie | Winchester, VA |
4. John Jacobs | Providence, RI |
5. Michael Leatherman | Norfolk, VA |
6. James Puckett II | Norfolk, VA |
7. Jay O'Donnell | Winchester, VA |
8. Paul Carpenter | Winchester, VA |