True or False?

You're taking your college entrance exam, and things are not going well. You spent too much time answering the essay questions and word problems, and now you're running out of time. You turn to the final section and are relieved to find that it consists of 100 True/False questions. The bad news is that you only have 2 minutes left to complete the entire exam!

You figure it doesn't matter if you answer all True, all False, or just guess randomly. Odds are you'll probably get half of them right either way. You begin scribbling in your answers.

How many different ways (unique sequences) are there to answer 100 True/False questions? Click below for the answer.

If you're a computer programmer, you may have recognized right away that this is just a binary counting problem in disguise. Substitute 1 for True and 0 for False, and this is the same as asking how many unique values can be represented by 100 binary bits. Since that's every value from all 0s to all 1s, the answer is $2^{100}$, or 1,267,650,600,228,229,401,496,703,205,376.