THE SOLUTION:
Colon batted first, folowed by Adams, Berry, and then Davis.
Clue #1 reveals that Davis did not bat first or second, and Berry did not bat first or last.
Clue #2 reveals that Adams did not bat first, which means Colon had to bat first. Since Adams batted next, he was second. By elimination, that leaves Berry in the third spot and Davis hitting fourth.
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