Challenge Accepted

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Across
  1. 4. Indecisive
  2. 6. Card-holding state
  3. 8. Alternate name for an ancient civilization
  4. 9. Reddish-hued lawman, say
  5. 13. Cowardly fowl, say
  6. 15. They bet on the wrong horse
  7. 16. Abbreviation for investigator or machinery
  8. 17. Animated sailor's fuel source
  9. 19. Bridal headwear capable of sheer concealment
  10. 20. A liberal sportsman, say
Down
  1. 1. The original nihilist
  2. 2. Politely tipsy, say
  3. 3. A town opposite itself
  4. 5. A place of worship and the start of a capital city
  5. 7. A Spaniard's method of questioning
  6. 10. Exact, strictly speaking
  7. 11. Italian river of historical significance
  8. 12. Metallic thievery, say
  9. 14. Incisal elimination, say
  10. 18. Namesake of a famous number