From the introduction, only the winning bull rider stayed on his bull the
required 8.00 seconds, for which he was credited with an 8.00second ride,
with the other four competitors each lasting a different amount of time on
his bull. By clue 1, the rider who had the shortest ride before being thrown
was on his bull 3.60 seconds. So, the range of rides was from 8.00 down to
3.60 seconds. By clue 4, Joe stayed on his bull twice as long as Spurrier.
By clue 7, Horn stayed on his bull twice as long as Rick. Since Rick and
Spurrier aren't the same cowboy (7) and no two bull riders stayed on their
bulls the same length of time, four different bull riders are named between
clues 4 and 7. Then either Joe or Horn had the 8.00second ride and/or
Spurrier or Rick had the 3.60second ride; otherwise, there would be at
least six different bull riders. If neither Joe nor Horn had the 8.00second
ride and Spurrier or Rick had to have ridden for 3.60 seconds, a third time
would have been 7.20 seconds (4, 7). For one of the remaining pair in
clues 4 and 7 not to have been the winner, one ride would have been between
7.20 and 8.00 seconds and the other 3.60 and 4.00 seconds. However, there
would then be no way for a difference of 1.60 seconds between two rides (2)
to work. So, either Joe or Horn did have the winning ride, and a third ride
was for 4.00 seconds (4, 7). For one of the remaining pair in clues 4 and
7 not to have had the shortest ride, one ride would have been between 3.60 and
4.00 seconds and the other then between 7.20 and 8.00 seconds. Again,
however, there would then be no way for a difference of 1.60 seconds between
two rides (2) to have occurred. So, in clues 4 and 7, either Spurrier or
Rick had the shortest ride of 3.60 seconds; and either Joe or Horn then
stayed on board his bull 7.20 seconds. Trying Horn as the winner of the
bull riding event, Rick would have ridden for 4.00 seconds (7), Joe for
7.20 seconds, and Spurrier for 3.60 seconds (4). By clue 5, either Cal
would be Spurrier or would be the fifth rider to the four already named.
If Cal were Spurrier, Buckley would have ridden his bull for 5.20 seconds (5).
By clue 2, Buckley would be Pete. Hank then would have won the bull riding
competitionwhich he did not (9). If Cal were the fifth rider, Buckley would
be Joe and Cal would have ridden his bull for 5.60 seconds (5). However, there
is no way for clue 2 to work given this arrangement. Therefore, Horn did
not win the bull riding contest; Joe did. Spurrier stayed on his ride for
4.00 seconds (4), Horn on his for 7.20 seconds, and Rick on his 3.60 seconds
(7). By clue 5, either Cal is Spurrier or the fifth rider to the four
already named. If Cal were the fifth rider to the four already named, Joe
would be Buckley in clue 5; and Cal would have stayed on his bull for 6.40
seconds. However, there is no way for clue 2 to work given this arrangement.
So, Cal is Spurrier; and by clue 5, Buckley rode his bull for 5.60 seconds.
If Pete in clue 2 were Buckley, Hank would be Horn and would have stayed on his
bull for 7.20 secondsno (9). Pete in clue 2 is Horn, and Hank Buckley rode
L'il Dynamite in the event. Joe didn't ride Hercules or Black Death (8).
Since Joe is either Gore or Roper, he also didn't ride Terror (3). Joe won
by staying on El Nasty. Joe is then Roper and Rick Gore (6). Neither Rick
(3) nor Cal (5) was on Terror's back, so Pete was. Finally, by clue 4, Rick
was on Hercules and Cal Spurrier on Black Death. In sum, the five competitors
in the Rainbow River Rodeo bull riding event finished as follows:
 Joe Roper, 8.00 sec. on El Nasty
 Pete Horm, 7.20 sec. on Terror
 Hank Buckley, 5.60 sec. on L'il Dynamite
 Cal Spurrier, 4.00 sec. on Black Death
 Rick Gore, 3.60 sec. on Hercules


