| From the introduction, each of the six girls got a different number
of the 3200 total votes cast, with the Prom Queen getting 800 votes to win;
while by clue 7, the girl who finished last in the contest got at least 80
votes. By clue 1, Lara had 240 more votes than the Torres girl, who garnered
twice as many votes as Nina; and by clue 3, the Wilson girl had 160 votes more
votes than Monica, who received twice as many votes as the Young girl did.
Since three girls are mentioned in each clue, either one or more of the girls
is common to the two clues or all six contestants are named between the
two. The possible commonality between the clues is that 1) Nina is the Wilson
girl, 2) that Lara is the Young girl, 3) that Lara is the Wilson girl, or
4) that Monica is the Torres girl and Nina the Young girl (since no two had
the same number of votes, Monica can't be Torres and Nina and Young be
different girls or vice versa). Trying the first possibility, that Nina is
the Wilson girl, if the Young girl had gotten only the absolute minimum of
80 votes (clue 7), Monica would have received 160, Nina Wilson 320 (3), the
Torres girl 640, and Lara 880 (1)--no, since the Prom Queen got 800 (intro).
Similarly, trying the second possibility,if Lara were the Young girl and
Nina got only the absolute minimum of 80 votes (7), the Torres girl would
have garnered 160, Lara Young would have gotten 400 (1), Monica would have
received 800, and the Wilson girl would have had 960 (3)--again contradicting the
introduction. Trying the third possibility, that Lara is the Wilson girl, by
clues 1 and 3, Nina would have received X votes, the Torres girl 2X, Lara
Wilson 2X + 240, Monica 2X + 80, and the Young girl X + 40--so that five of
the six contestants are named and either Lara or the sixth girl would have
won the contest. If Lara Wilson had won with 800 votes (intro), then
2X + 240 = 800 and X = 280. Lara Wilson would have had 800 votes, Monica 640,
the Torres girl 560, the Young girl 320, and Nina 280--a total of 2600, so
that the sixth girl would have gotten 600 votes. However, there is no way
for clue 6 to work given these totals. If the sixth girl had won with 800
votes, then the five girls in clues 1 and 3 would have had 2400 votes among
them, so that 8X + 360 = 2400 and X = 255. The sixth girl would have had
800 votes, Lara Wilson 750, Monica 590, the Torres girl 510, the Young girl
295, and Nina 255. Again, however, there is no way for clue 6 to work given
these totals. So, Lara is not the Wilson girl. Trying the fourth possible
overlap, that Monica is the Torres girl and Nina the Young girl, Nina Young
would have gotten X votes, Monica Torres 2X, the Wilson girl 2X + 160, and
Lara 2X + 240. Lara isn't the Roman girl (5), who would be a fifth girl to
the four in clues 1 and 3. Heidi isn't the Wilson girl or the Roman girl (6),
so she would be the sixth contestant. Either Lara or Heidi then would have
won the contest. If Lara had received 800 votes, 2X + 240 = 800 would give
X = 280, so that Nina Young would have gotten 280 votes, Monica Torres 560,
and the Wilson girl 720--a total of 2360 and leaving 840 for Heidi and the
Roman girl. By clue 6, Heidi would have gotten 460 and the Roman girl 380
votes. However, Jana finished 4th in the balloting (8), impossible given
these totals. If Heidi had won with 800 votes, the Roman girl would have
gotten 720 (6), leaving 1680 for the other four contestants. If Lara had
gotten more than 720 votes, the Wilson girl would have gotten more than 640,
Monica Torres more than 480, and Nina Young more than 240--a total of more
than 2080 and not possible. So, Lara would have gotten fewer votes than the
Roman girl. Then Jana would be the Wilson girl (8) and Kerrie the Roman
girl--no (2). So, the fourth possible overlap also fails. Therefore, there
is no overlap between clues 1 and 3 and all six girls are named between the two
clues. Either Lara or the Wilson girl then was elected Prom Queen with 800 votes.
If Lara had won, the Torres girl would have gotten 560 votes and Nina 280
(1), a total of 1640 and leaving 1560 for the girls in clue 3. In clue 3,
the Young girl got X votes, Monica 2X, and the Wilson girl 2X + 160--a total
of 5X + 160 = 1560 or X = 280. The Young girl would have received 280
votes, the same as Nina and a conflict with the introduction. So, the
Wilson girl was elected Prom Queen with 800 votes, Monica received 640 votes,
and the Young girl ended up with 320 (3), a total of 1760 and leaving 1440
for the three in clue 1. In clue 1, Nina got X votes, the Torres girl 2X,
and Lara 2X + 240--a total of 5X + 240 = 1440 or X = 240. Nina got 240,
the Torres girl 480, and Lara 720 votes in the balloting. By clue 8, Jana
is the Torres girl. Heidi is the Young girl (6) and Kerrie Wilson. The
Roman girl is Nina (6). Finally, by clue 4, Monica is the Vincent girl and
Lara Stone. In sum, the contest for Summerset High Prom Queen finished
- Kerrie Wilson -- 800
- Lara Stone -- 720
- Monica Vincent -- 640
- Jana Torres -- 480
- Heidi Young -- 320
- Nina Roman -- 240
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