| From the introduction, each attempt to win a prize at the Midway games cost
$1, with a total of $35 spent by the five before each succeeded in winning
a stuffed animal. By clue 8, the fastest anyone won a prize was throwing
the Ring Toss, where one teen won for $2. By clue 2, the friend who won
the stuffed hippo spent $10 to do so. By clue 1, Theo spent twice as much
to win as the one who got the stuffed alligator; while by clue 4, Sammy
took twice as many chances to win as the teen who won playing the Pro QB
football throw. Since the one who got the stuffed alligator didn't win it
at the Ring Toss (clue 5), none of those in clues 1 and 4 won at that game.
Therefore, between clues 1 and 4, either all four remaining teens are named
or there is overlap--either Theo won at Pro QB or Sammy won the stuffed
alligator. Trying the overlap case first, we combine clues 1 and 4 to designate
the teens by the amounts they spent as X, 2X, and 4X. If none had won the hippo
for $10, they would have spent $23 among them ($35-$10 for the hippo and $2 at
the Ring Toss) so that 7X would equal $23--impossible since X would not equal
an even dollar amount. So, one of the three would have had to have won
the stuffed hippo. If the one who spent X had won the stuffed hippo,
then the other two would have tried 20 and 40 times--no, the total was 35.
If the one who spent 2X had spent the $10, then the others would have
spent $5 and $20 and again the total for the five would exceed $35. If
the one who spent 4X had won the hippo for $10, then the one who spent X
would have spent $2.50--no from the introduction. Therefore, there is no
way for clues 1 and 4 to overlap; and we have four different teens named:
Theo who spent twice what the alligator winner did and Sammy who spent
twice what the one who won at Pro QB did. Since we earlier established
that none of the four played Ring Toss, one of the four had to have
won the stuffed hippo. If either the one who won the stuffed alligator or
the one who played Pro QB had spent $10 to win the hippo, Theo or Sammy
would have spent $20--a total of $32 including the Ring Toss player,
leaving $3 for the other two to spend at $2 and $1 each--no (8). So,
either Theo or Sammy won the hippo for $10 and either the one who won the
stuffed alligator or the one who played Pro QB spent $5 to do so. This
gives a total of $17 with the Ring Toss, leaving $18 for the other pair,
so that 2X plus X equals $18, or X equals $6. The other two sums are $12
and $6. By clue 3, the friend who won at HydroJets spent $5 more than the
one who took home the stuffed snake; the only possible way for this to work
is for the one who won at HydroJets to have won the hippo for $10 and the
teen who won the snake to have spent $5. Then in clues 1 and 4, the snake
had to have been won at the Pro QB booth, with Sammy winning the hippo;
Theo spent $12 and the winner of the stuffed alligator $6. Theo didn't win
the stuffed donkey (7), which went to the Ring Toss player; Theo won the
panda--at the Goose Pond (6), with Bull's-Eye Balloons being where one
teen won the stuffed alligator. Neither Leah (3) nor Eric (4) won the
stuffed snake throwing the football at Pro QB, so Marcie did. By clue 7,
Leah won the alligator for $6 and Eric the stuffed donkey. In sum, the
five teens won stuffed animals as follows:
- Eric won a donkey at the Ring Toss for $2
- Marcie won a snake at Pro QB for $5
- Leah won an alligator at Bull's-Eye Balloons for $6
- Sammy won a hippo at HydroJets for $10
- Theo won a panda at the Goose Pond for $12
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