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Full bracket posted.

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The two "if" sentences in 2b carry the same weight because they both cannot happen at the same time.

Doesn't matter anyway.

Rice fouls with 3.2 left. 3rd Rice foul of the quarter.

Rice wins 47-45.

Rice 47-45 6.2 left NT ball.

3-way does not exist after conducting the round-robin because MT is removed from the tie.

Rice ball with 7.4 left after a jump ball. Still 46-45 Rice.

Rice 46 NT 45 :31.2 left NT ball

Because that's exactly what the tiebreaker rules say. Read the bolded section of 2b. Middle Tennessee would be removed from the tie getting #3 seed leaving a 2-way tie between Charlotte and Tech.
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We have the answer to the thread title question...no.

Tech is #3 seed if Rice wins. #5 if Rice loses.

3-way tie without Rice--MT 2-1, Tech 1-1, Charlotte 1-2. MT is #3. #4 would go to Charlotte...