The sun climbed over Destiny Downs racetrack. It cast long shadows on the spotless grass where seven superb horses would soon race in the season’s most awaited event: the Derby of Destiny. This wasn’t an ordinary race—it had a mathematical puzzle that had left racing fans scratching their heads for weeks.
Meet the Superb Seven
Seven top horses stood ready, each with their own outstanding racing background:
Thunder (A) – The ruling powerhouse with jet-black fur
Blaze (B) – The fiery chestnut with super-fast speed
Champion (C) – The battle-tested pro with tons of wins
Dazzle (D) – The showy rookie who wowed crowds
Eclipse (E) – The enigmatic underdog who trailed rivals
Flash (F) – The silver blur known for last-minute surges
Glory (G) – The golden victor aiming for ultimate triumph
Racing Records Reveal a Pattern:
- Thunder (A) beats Blaze (B) – 10 out of 10 times
- Champion (C) beats Thunder (A) – 8 out of 10 times
- Dazzle (D) beats Champion (C) – 7 out of 9 times
- Eclipse (E) beats Dazzle (D) – 6 out of 8 times
- Flash (F) beats Eclipse (E) – 5 out of 7 times
- Glory (G) beats Flash (F) – 4 out of 6 times
- Blaze (B) beats Glory (G) – 9 out of 11 times
Challenge: Using these direct and derived relationships, determine which horses are likely to win the next race.
View the answer
Derived Cross-Relationships:
Based on transitive performance (if X beats Y and Y beats Z, then X’s likelihood against Z = X’s rate × Y’s rate = 7/9 × 8/10):
- Champion (C) beats Blaze (B) – 8 out of 10 times (via Thunder)
- Dazzle (D) beats Thunder (A) – 6 out of 10 times (via Champion)
- Eclipse (E) beats Champion (C) – 5 out of 9 times (via Dazzle)
- Flash (F) beats Dazzle (D) – 4 out of 8 times (via Eclipse)
- Glory (G) beats Eclipse (E) – 3 out of 7 times (via Flash)
- Blaze (B) beats Flash (F) – 6 out of 11 times (via Glory)
Analysis Method: Each horse’s overall performance is calculated by averaging their win rates against all other horses (using both direct and derived matchups).
Individual Horse Performance:
Thunder (A):
- Beats Blaze 10 out of 10 times
- Loses to Champion 2 out of 10 times
- Loses to Dazzle 4 out of 10 times
- Loses to Eclipse 1 out of 7 times
- Loses to Flash 2 out of 11 times
- Loses to Glory 1 out of 11 times
- Average win rate: 13.2%
Blaze (B):
- Loses to Thunder 0 out of 10 times
- Loses to Champion 2 out of 10 times
- Loses to Dazzle 1 out of 9 times
- Loses to Eclipse 1 out of 7 times
- Beats Flash 6 out of 11 times
- Beats Glory 9 out of 11 times
- Average win rate: 12.8%
Champion (C):
- Beats Thunder 8 out of 10 times
- Beats Blaze 8 out of 10 times
- Loses to Dazzle 2 out of 9 times
- Loses to Eclipse 5 out of 9 times
- Loses to Flash 2 out of 6 times
- Loses to Glory 4 out of 11 times
- Average win rate: 19.6%
Dazzle (D):
- Beats Thunder 6 out of 10 times
- Beats Blaze 8 out of 9 times
- Beats Champion 7 out of 9 times
- Loses to Eclipse 2 out of 8 times
- Loses to Flash 4 out of 7 times
- Loses to Glory 3 out of 6 times
- Average win rate: 20.0%
Eclipse (E):
- Beats Thunder 6 out of 7 times
- Beats Blaze 6 out of 7 times
- Beats Champion 4 out of 9 times
- Beats Dazzle 6 out of 8 times
- Loses to Flash 2 out of 7 times
- Loses to Glory 3 out of 6 times
- Average win rate: 18.0%
Flash (F):
- Beats Thunder 9 out of 11 times
- Loses to Blaze 5 out of 11 times
- Beats Champion 4 out of 6 times
- Beats Dazzle 3 out of 7 times
- Beats Eclipse 5 out of 7 times
- Loses to Glory 2 out of 6 times
- Average win rate: 18.8%
Glory (G):
- Beats Thunder 10 out of 11 times
- Loses to Blaze 2 out of 11 times
- Beats Champion 7 out of 11 times
- Beats Dazzle 3 out of 6 times
- Beats Eclipse 4 out of 6 times
- Beats Flash 4 out of 6 times
- Average win rate: 20.0%
Final Rankings:
Dazzle (D): 20.0% – Tied for highest average win rate
Glory (G): 20.0% – Tied for strongest overall performance
Champion (C): 19.6% – Close third with solid matchups
Flash (F): 18.8% – Strong mid-tier performer
Eclipse (E): 18.0% – Decent against most opponents
Thunder (A): 13.2% – Perfect against Blaze but poor elsewhere
Blaze (B): 12.8% – Weakest overall record
Key Insight: Despite Thunder’s perfect record against Blaze, the transitive relationships reveal Dazzle and Glory as favorites for the coming event, showing how circular dynamics can differ from apparent perspectives.
