|By clue 3, Tubbs finished one place higher than the cowboy who won the
barrel racing in the overall championship standings. By clue 1, Toby
finished higher in the overall than Beggs. Given that Beggs didn't win
the barrel racing (clue 5) and that Toby isn't Tubbs (7), there are five
ways to combine the two clues: (1) Tubbs placed 1st, the barrel racing
winner 2nd, Toby 3rd, and Beggs 4th; (2) Tubbs placed one position ahead
of barrel race winner Toby, who was one position ahead of Beggs; (3) Tubbs
finished 1st, barrel race winner Toby 2nd, and Beggs 4th; (4) Toby was 1st,
Tubbs 2nd, the barrel race winner 3rd, and Beggs 4th; or (5) Toby won the
overall championship, Beggs placed 2nd, Tubbs 3rd, and the barrel racing
winner 4th. Trying (1), Monty would be Tubbs (8). Monty won neither the
calf roping nor bull riding title (4, 8) and would have won the bronco busting.
This conflicts with clue 2. So, (1) fails. Trying (2), by clue 8, Monty
would have finished 1st with Tubbs 2nd; or Monty would have been 4th with
Beggs 3rd. In the first case, Monty won neither the calf roping nor bull
riding title (4, 8) and would have won the bronco busting--no (2). In the
second case, Potts would have been 2nd (2) and Mimms would be Monty.
However, Monty won neither the calf roping nor bull riding (4, 8) and would
have won the bronco busting, a conflict with clue 6. So, (2) fails.
Trying (3), Monty would be Beggs (8) and would have won the bronco busting
(4, 8). By clue 6, Jesse would be Tubbs. However, Charlie isn't Mimms or
Potts (9). So, (3) fails. Trying (4), Jesse would be Tubbs, and Mimms
would have placed 3rd. The bronco busting champ would have placed 4th
overall (2, 6). However, neither Toby (7) nor Jesse Tubbs (4) could have won
the calf roping. So, (4) fails; and we have (5): Toby won the overall
championship, Beggs placed 2nd, Tubbs 3rd, and the barrel racing winner 4th.
The calf roping winner isn't Toby (7) and didn't place 2nd (4), so he is Tubbs.
Toby is Potts, and Beggs won the bronco busting event (2). By elimination,
Toby won the bull riding event, and Mimms placed 4th overall. By clue 6,
Jesse is Tubbs. Monty is Mimms (8) and Charlie Beggs. In sum, the Summerset
County Rodeo overall championship standings were
- 1st, Toby Potts, bull riding
- 2nd, Charlie Beggs, bronco busting
- 3rd, Jesse Tubbs, calf roping
- 4th, Monty Mimms, barrel racing