Minigames

**Please refer to the Exponential Idle Guides for strategies. This wiki should only be used as a lookup table for equations and other game elements. The proper Minigame Guide is better and has actual strategies. For the Arrow puzzle, use this PDF guide for visuals.**

Minigames are one of the various ways to gain additional stars and achievements. Currently, there are two minigames. There is the 15-Puzzle, a sliding puzzle, and Torus Puzzle (inspired by Loopover and RotSquare), a 2D version of the Rubik's Cube.

Since the 1.4 update, a third minigame has shown up, Arrow.

## 15-Puzzle

There are various strategies used for the slide puzzle. One strategy is to do the top row, followed by the left column, and repeat these two steps for smaller and smaller n x n areas of the board until you end up with a 2-by-2 area. After that, continuously "spin" in either the clockwise or anticlockwise direction within the remaining 2-by-2 area to complete the puzzle (i.e. slide the remaining 3 tiles along clockwise/anticlockwise continuously). The solved patterns are shown below. Here is a great website that explains how to do it. Exponential Idle Minigames Guides

Easy - Goal State, awards 1 star

 4
 7

Medium - Goal State, awards 3 stars minimum

 5
 9
 13

Hard - Goal State, awards 6 stars minimum

## Torus Puzzle

Note: This section is incomplete, and requires more editing. **Best strategies can be found on the Exponential Idle Minigame Guides.**

Also referred to as a 2D Rubik's Cube and Loop Over, this puzzle in the Easy 3x3 size is almost trivial with some basic techniques, but at scale becomes significantly more challenging.

### Method (displayed on Medium)

**Step 1. Align First Row** - Get the top row in order. (does not matter the position of any other number)

**Step 2. Fill in the Columns** - The goal of this step is to complete all the rows but the last the techniques can be applied for all rows except the last.

Techniques

Basic Maneuvering to Column

Manuevering around an in placed piece

**Step 3. Order Last Row** - Order the last row with respect to the smallest value

\*Repeat the process to position the bottom row to place the X\* with respect to the smallest value until all values have been placed

**Step 4\*. Parity Correction** (only needed on Hard difficulty) - shift all values in the bottom row over one position using step 3 technique

Just cycle each number over one by one and the bottom row will align and all other tiles will be in place. (may need to slide the bottom into position depending on where you began)

Easy - Goal State, awards 1 star

 4
 7

Medium - Goal State, awards 8 stars minimum

Hard - Goal State, awards 14 stars minimum

## Arrow

A compiled PDF guide with screenshot visuals is available!

The goal of this minigame is to have all the arrows pointed upwards. There are four levels of difficulty :

* Easy : 3 by 3 square, 4 possible orientations
* Medium : 4 by 4 square, 4 possible orientations
* Hard : hexagonal pattern of side length 4, 2 possible orientations
* Expert : hexagonal pattern of side length 4, 6 possible orientations

On a square grid, whenever an arrow is touched, it will rotate 90° clockwise along with all its neighbours. The neighbours are all arrows in a 3 by 3 square centered around the touched arrow, there are less neighbours when you touch an arrow on an edge or a corner (ie the board is not a torus).

On the hexagonal grid, the neighbours are all adjacent arrows (up to 6). On the Hard difficulty, the arrows flip between up and bottom orientation when touched, on Extreme, they rotate by 60° clockwise.

### Convention

Instead of arrows, these tutorials exclusively use numbers, viewable if you click the settings button, and then, select Display Mode: Numbers. In each case, an arrow pointing upwards is represented by 1 and when you tap on an arrow, it means that you add 1 to its value and the value of all its neighbours. A minus means that we don't know the orientation.

Easy and Medium:  1 means that the arrow is pointed up, 2 means right, 3 means down and 4 means left.

Hard:  1 means that the arrow is pointed up, and 2 means down.

Expert:  1 means that the arrow is pointed up, 2 means 60° (right, slightly upwards), 3 means 120° (right, slightly downwards), 4 means down, 5 means 240° (left, slightly downwards) and 6 means 300° (left, slightly upwards).

### Strategy for the Easy puzzle

**Step 1 :** Arrange a 2 by 2 square on the bottom right with only ones, the leftmost column and topmost row are still to be taken care of.

**Step 2 :** Arrange all missing values except the top left corner with the following patterns. The numbers in the first grid represent how much to tap on each square, the numbers on the right represent the change in the arrows orientation :

→

{\displaystyle \rightarrow}

 0
 0

→

{\displaystyle \rightarrow}

 0
 0

→

{\displaystyle \rightarrow}

 0
 0

The 3 presented pattern can be shifted to change the values of the whole column or only the 2 top values. They can also be transposed to change the values of the top row. After this step, only the top left corner might not point upwards.

**Step 3 :** Use one of the following patterns to change the orientation of the top left corner.

→

{\displaystyle \rightarrow}

 0
 0

→

{\displaystyle \rightarrow}

 0
 0

→

{\displaystyle \rightarrow}

 0
 0

### Strategy for the Medium puzzle

This strategy is globally the same as for the Easy puzzle with only a bit more complex patterns.

**Step 1 :** Arrange a 3 by 3 square on the bottom right with only ones, the leftmost column and topmost row are still to be taken care of.

**Step 2 :** Arrange all missing values except the top left corner with the following patterns. The numbers in the first grid represent how much to tap on each square, the numbers on the right represent the change in the arrows orientation :

The 3 presented pattern can be shifted to change the values of 3 values in the column or only the 2 top values. They can also be transposed to change the values of the top row. After this step, only the top left corner might not point upwards.

**Step 3 :** Use one of the following patterns to change the orientation of the top left corner.

### Strategy for the Hard and Expert puzzles

It is strongly recommended to use the PDF version of the guide *with in-game visuals*.

**Preliminary - Definition of "Propagation"**

*NOTE: This is not the full solution. This explains the "propagation" part of the solution.*

Although this puzzle is often not fully solvable by simply solving row by row, we can solve it except the bottom row. We call this "propagation". This is how we perform it:

**Main Idea:** To make a tile into a 1, tap the tile below it. (*Note for general algorithm: avoid tapping the top tiles since they will affect further algorithm)*

Steps:

1. Find the uppermost tile that is not 1.
2. Tap the tile under it to make the tile into 1.
3. Find the new uppermost tile that is not 1. Repeat steps 1 and 2 until all tiles, except the bottom-most tiles, are all 1.

Example iteration of this method (click "Expand" to the right):
Underscores indicate unknown tiles.

**Full Strategy of Hard and Expert Puzzles**

The below table shows the locations of tiles we will refer to as a, b, c, d, A, B, C, D.

Underscores indicate irrelevant tiles.

Steps:

1. Propagate
2. Encode
	1. Tap **a** so that **a** is the same as **C**
	2. Tap **b** and **d** the number of times you would need to solve **C**
	3. Tap **a** the number of times you would need to solve **D**
	4. If **B** + **D** is odd, tap **c** three times (once in hard)
3. Propagate (do not tap any of the top 7 tiles on the board)

## Rewards

The formula for stars given by a game is floor(gameBaseReward \* max(1, 0.02 \* dt^0.5)), where gameBaseReward is the initial number of stars given by the game. Note: 0.02 \* sqrt(dt) is the expansion of 50.0 \* starChance.