Imagine you’re standing on an endless chessboard, your own little universe of squares stretching infinitely in all directions. Your coordinates right now are (3, 4). This is your starting point, and you’re feeling adventurous. But there’s a specific spot you want to reach: the point (6, 8). A friend told you that the key to navigating this grid is all about finding the most efficient path, and you really want to get there in the least number of steps possible.

Now, here’s the catch: you can move in any direction you want. You can step up, down, left, right, or even diagonally, and every single move counts as one step regardless of the direction. This creates all sorts of possibilities for you! You’re not restricted like a knight in chess; instead, you have free reign to find your way across this infinite expanse.

To get you thinking, let’s break down your journey a bit. If you were to move straight up, you’d only be inching towards your destination. Similarly, if you went directly to the right, you’d miss out on closing the gap vertically. But what if you used a diagonal move instead? It feels like there are a ton of different routes.

Now, here’s where I want to hear your thoughts: how would you plan your route? What path would you take from (3, 4) to (6, 8)? How many steps do you think it’ll take? I know it’s tempting to just map it out in your head, but take a moment to consider all the options. You can visualize it as a game, or maybe even create mini-strategies for each move.

Let’s put your reasoning to the test. How would you tackle this? What’s the minimum number of steps you think you’ll need to reach that target point? Share your thought process with me; maybe there’s a hidden shortcut we both haven’t considered.