I was recently interviewing at a company. I got a hint that the hiring manager liked to ask brain teasers. I like the challenge. I ended up muddling through it, but the challenge went like this:
You have 3 ants, each on a corner of a triangle. What is the probability that all of the ants would move in the same direction?
Thinking about it, the problem had a sort of binary representation. So I started writing out the various combinations: 111, 110, 100, 000, 001, 011, 010, 101. That's 8 possibilities. Adding another corner would produce a square with 4 ants, which would have 16 possible outcomes. With each bit, we double the number of possibilities.
That's about where I landed. I had an intuitive understanding of it, but I couldn't articulate the probability clearly at the time. I was able to work through it, but at the end of the day I'm reminded that math isn't my strongest suit.
Later, I found out the answer is 1/4. Each ant has 2 choices (clockwise or counterclockwise), so there are 2³ = 8 total outcomes.. That's exponentiation. Only 2 of those (All clockwise or all counterclockwise) have everyone moving the same direction. So 2/8 = 1/4.