| By clue 1, among the five radio personality duos 115 total foot-longs
were consumed, with the least any team eating being 10. By clue 2,
Kirk and his partner ate 10 more foot-longs than the pair from WRST-FM
and 20 more than Amelia and her partner; while by clue 5, Mark and his
partner ate twice as many hot dogs as the WPOP-FM duo, who ate 10 more
foot-longs than Jones and partner. Since six pairs are named between
the clues, one or more must overlap. We will test the three in clue 5
as being in common with the three in clue 2. If Kirk and Jones were
a pair, Amelia and her partner would have eaten 10 foot-longs, the duo
from WRST-FM would have had 20, Kirk and Jones would have had 30 (clue
2), the WPOP-FM team would have had 40, and Mark and his partner would
have eaten 80 (5)--a total of 180 and a conflict with clue 1. If Jones
were one of the WRST-FM personalities, Amelia and her partner would
have eaten at least 10 foot-longs, Jones and partner would have
had at least 20 (2), the WPOP-FM duo would have had least 30, and Mark
and his mate would have had at least 60 (5)--a total of 120 among the
four pairs and too much for clue 1. If Jones and Amelia were a pair
and had at least 10 hot dogs, the WRST-FM team would have had at least
20, Kirk and his partner would have had at least 30 (2), the WPOP-FM
personalities would have had at least 20, and Mark and his on-air
partner would have eaten at least 40 (5)--again too many at 120. So,
Jones and partner are the fourth pair to the three in clue 2.
If one of the WPOP-FM pair in clue 5 were Kirk in clue 2, Amelia
would have had at least 10 foot-longs, the WRST-FM duo would have
consumed at least 20, Kirk and his WPOP-FM partner would have had at
least 30 (2), and Mark and his mate would have downed at least 60,
a total of 120 among the four and too many (1). If Mark in clue 5
were Amelia's partner in clue 2, Jones and partner would have
eaten 10 hot dogs, the WPOP-FM pair would have downed 20, Mark and
Amelia would have had 40 (5), the WRST-FM team would have wolfed down
50, and Kirk and his partner would have eaten 60 (2)--summing to 180
and too many (1). If Mark were one of the WRST-FM personalities,
Jones and partner would have eaten 10 Ethan's Famous, the WPOP-FM
duo would have had 20, the WRST-FM duo would have consumed 40 (5),
Amelia and her partner would have downed 30, and Kirk and his pal
would have eaten 50 (2)--too many at 150. If the WPOP-FM duo
in clue 5 included Amelia in clue 1, Jones and pal would have had 10
of Ethan's Famous, Amelia and her WPOP-FM partner would have eaten 20,
Mark and his pal would have consumed 40 (5), the duo on WRST-FM would
have eaten 30, and Kirk and his partner would also have eaten 40.
If Kirk and Mark weren't partners, the total of 140 would contradict
clue 1. Kirk and Mark would have to be partners, and the four pairs
would have totaled 100 hot dogs, leaving 15 for the fifth on-air pair.
Trying Kirk and Mark as a pair, Jones and friend would have had 10
hot dogs, the WPOP-FM duo would have had 20, Kirk and Mark would
have eaten 40 (5), the WRST-FM duo would have downed 30, and Amelia
and mate would have consumed 20 (2)--a total of 120 and too many unless
Amelia is on WPOP-FM, leaving 15 foot-longs to have been eaten by the
fifth duo. This is the same result as above, so the overlap between
clues 2 and 5 is twofold: Kirk and Mark are partners, and Amelia is
on WPOP-FM. By clue 6, Mickey is one of the WRST-FM duo, and the
pair who ate 15 foot-longs is on WHAM-FM. By clue 3, Brian isn't
partners with Jones and isn't on WHAM-FM; while by clue 7, Brian isn't
Mickey's mate. Brian is Amelia's on-air partner. By clue 7, the
Hamster teams with Mickey. Lance is on WHAM-FM (4)--with Vince (9).
Cass is Jones' partner on WELL-FM (8), and Kirk and Mark are the
WDXW-FM duo. In sum, the results of the Ethan's Famous Foot-Longs
eating contest are
- 1st -- Kirk & Mark, WDXW-FM, 40
- 2nd -- Mickey & the Hamster, WRST-FM, 30
- 3rd -- Brian & Amelia, WPOP-FM, 20
- 4th -- Lance & Vince, WHAM-FM, 15
- 5th -- Cass & Jones, WELL-FM, 10
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