Minecraft Dimensional Analysis

Introduction

Right now in chemistry, we're using dimensional analysis to work with chemical equations. It's pretty cool, I think. The best part of using dimensional analysis is that it's applicable to almost anything, including Minecraft. Don't believe me? I can show you.

Situation

I'm on a Minecraft Realm (like a group world if you aren't familiar with the game) and I'm gathering materials for a HUGE house. The materials list for this build is incredible. As an example, last night, I collected 65 stacks and 41 blocks of spruce planks. That's \( (64 \times 65) + 41 = 4201 \) blocks. Yeah, it took like 5 hours. Either way, now my problem is to craft 4 stacks and 58 blocks of "nether brick fence," a type of fence:

Its crafting recipe is:

which we'll represent as the "chemical" (haha) equation:

\[ \text{2 nether brick + 4 nether bricks} \longrightarrow \text{6 nether brick fence}. \]

My goal is to use the minimum amount of nether bricks to only mine the netherrack I need to be efficient (yes, I know, writing this is probably the least efficient thing to do).

In any case, we can start by converting our desired amount of nether brick fence from a stack count to a block count:

\[ \text{4 stacks and 58 blocks} = \text{4(64) + 58 blocks} = \text{314 blocks nether brick fence} \]

Before finding how many nether bricks we'll need, here's dimensional analysis at its core:

\[ \cancel{\text{given unit}} \cdot \frac{\text{desired unit}}{\cancel{\text{given unit}}} = \text{desired unit} \]

Now, we can finally use dimensional analysis by starting with our given unit, 314 blocks of nether brick fence, to find our desired unit, nether bricks!

\[ \text{314 blocks} \cancel{\text{nether brick fence}} \cdot \frac{\text{4 nether bricks}}{\text{6 } \cancel{\text{nether brick fence}}} = \frac{628}{3}\text{ nether bricks} \approx \text{209.33 nether bricks} \]

Woohoo! Rounding up to the nearest whole number, we arrive at \(\text{210 nether bricks}\).

Now we know how many nether bricks to craft so we don't waste any resources! Super cool!

While this problem could probably be done by an elementary schooler who has a knack for problem-solving, dimensional analysis helps us not screw things up. Next time you're playing Minecraft, use it!