An ellipse passes through the points (0,-1), (2,0), (-2,2) and encloses minimum possible area. Find the equation of the ellipse.
Three six-member cross-country race teams hold a race. The 18 racers run simultaneously, and individually finish in 1st, 2nd, 3rd, ... , 18th place; there are no ties. The winning team is decided by which has the lowest total of place values of its first four placers, so that if a given team had members placing, say, 1st, 4th, 9th, 10th, 12th and 17th, that team's total would be 1+4+9+10=24. Again, a low team score therefore beats a high score.
In this race, no two of the three teams had the same score, and the third team's score was a multiple of the second team's score, which itself was a multiple of the winning team's score.
The sum of the positions (places) of the first three finishers on the winning team was the same as the total of the first two finishers on the second team. It also matched the place number of the first finisher on the third team.
What teams did each of the 18 place finishers belong to?
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