If there were 1 question, there would be two possible sequences: T or F
If there were 2 questions, there would be 4 possible sequences: TT TF FT FF
So, if there were n questions, each can be answered in 2 ways, so you have 2^n possible sequences.
Note: your question was not T/F. The quiz had T/F questions. Your job was to prove that 1024 was the correct answer.
Since the question itself said that the answer is 1024, that was good reasoning to think that 182 was wrong. :-)
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