# Perfectly Balanced Basic Gameplay Guide

In case the game doesn’t make it clear enough about some rules. This guide does not provide any solutions, so you won’t get spoiled.

# Basic Rules

The game has only a few rules.

1. You have a finite amount of weight that must be placed. (Your “kg” must be 0.)

2. You have a finite number of blocks that must be placed. (Your “blocks” must be 0.)

3. You must balance the two sides. (Check marks ✅ on both sides)

4. You cannot go beyond a specific height or width at any time. (“Not enough space.”)

5. You cannot place heavier object over a lighter one. (“Too heavy.”) But, you may build a tower as high as you need, as long as no object is heavier than the one below.

The rules are NOT introduced explicitly.

# 1: Weight Difference

First, find the weight difference between the two sides.

You don’t need to care about the actual weights of each side, just the difference.

For example, see the following figure (do you still use ASCII arts?):

``` ___ o
/ \----------\
/ \ \---------___
/1 \ / \
--------- /2 \
/ 3 \
-----------
```

The weight difference is 4 to the right, or I usually write it as +4, but it doesn’t matter. Keep this number.

The actual weight doesn’t matter, but you need to look at the puzzle picture to see how much weight can be placed. Sometimes the puzzle is designed to prevent you from putting large objects. We will handle this in a later section.

# 2: (VERY SIMPLE) Solve for Required Weight on both sides

Now, we will do one very simple math.

You must put {half of the sum of weight required (top right of your screen) and weight difference between the two sides} onto the lighter side.

In this case, if the sum of weight required is 8, and (based on section 1) the weight difference is 4, you should add (8+4)/2 kg to the LIGHTER side.

This is what the solution looks like if the game requires 2 blocks to be added (the bracketed numbers are the added blocks):

``` _____________o______________
/ \ / \
/ \ /2 \
/ 1 [6] \ / 3 [2]\
----------- -----------
```

Mathematical proof (#TheyDidTheMath) will be provided in the appendix.

# 3: Puzzle Time: How to fit the weight

Following the game rules, now you have to divide the weight allocated to each side into blocks.

For this part, human intuition is easier than mathematical proof, so I’ll just let you do it. Remember to follow the rules in the introduction. Some rules of thumb are:

• Prioritize placing heavier blocks first. Heavy blocks are harder to place.
• You can always cut 6 into 5+1. Not so easy to change your 5+1 into a 6 (because the structure below it might be limited to 5 kg).

Pro tip: You can click anywhere on the screen to drop something. I spent 2 minutes like an idiot trying to pull the weight from the top right.

# Appendix A: Mathematical Proof to Section 2

Here is a proof that the solution in Section 2 is mathematically correct.

Let A be an integer > 0 representing the weight amount given to the player (top right of the screen)

Let D be an integer >= 0 representing the weight difference between the two sides of the scale.

Let X and Y (both integers > 0) be the weight you need to add to the lighter and the heavier sides respectively.

Based on the rule of the game, we know that:

X + Y == A ——– [1]

We also know that we need to balance the weight by making up the difference between P and Q, such that:

X – Y == D ——– [2]

By adding [1] + [2] together, we will achieve:

2X == A + D

X == (A + D) / 2

You can solve trivially for Y using equation 1.

This means the weight added to the light side is “half of the sum of the weight given by the game and the weight difference between the two sides of the scale”. QED.