Puzzle o' the Day 411!
Here's a cute one I got from one of my sources. Yes, I have sources.
You're going to take a random walk! Unlike most random walks, however, the length of each step will *not* be constant. Instead, the length of the first step will be 1/2, the length of the second step will be 1/4, then 1/8, 1/16, and so on. As usual, we'll flip a coin before each step, which will determine the step's direction.
1. (Medium-easy). Say "heads" means "East" and "tails" means "West". On average, how far will you end up from your starting position?
2. (The puzzle: medium). Say "heads" means "East" and "tails" means "North". On average, how far will you end up from your starting position?
You're going to take a random walk! Unlike most random walks, however, the length of each step will *not* be constant. Instead, the length of the first step will be 1/2, the length of the second step will be 1/4, then 1/8, 1/16, and so on. As usual, we'll flip a coin before each step, which will determine the step's direction.
1. (Medium-easy). Say "heads" means "East" and "tails" means "West". On average, how far will you end up from your starting position?
2. (The puzzle: medium). Say "heads" means "East" and "tails" means "North". On average, how far will you end up from your starting position?