what is half of 222?

You should be able to get this in half a second.

Highlight between the brackets (see below) to see the explanation. After I thrash you a thousand times with a foot-long centipede because you didn't get the answer. How, ninnyhammer? How could you not—get—the answer?

[EXPLANATION: the correct answer, according to the multiple-choice question in the video, is (b). These are all powers of 2, right? If you take the exponent down by one, you've taken the number it represents—the result—down by a half. Let me walk you through this:

base^exponent = result

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

So as you see above, the difference between 2^x and 2^x+1 is a factor of 2. Same for the difference between 2^x and 2^x-1. So if know that 2⁵ = 32, then 2⁴ has to be half that, i.e., 16. 

By this logic, half of 2²² is one exponent lower: 2²¹. On the video, the answer is (b). QED.]