Minigames

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. http://www.kopf.com.br/kaplof/how-to-solve-any-slide-puzzle-regardless-of-its-size

Easy - Goal State, awards 1 star Medium - Goal State, awards 3 stars minimum Hard - Goal State, awards 6 stars minimum

Torus Puzzle
Note: This section is incomplete, and requires more editing.

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 Medium - Goal State, awards 8 stars minimum Hard - Goal State, awards 14 stars minimum

Arrow
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 : 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.

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 puzzle
Step 1:  Click on any cell directly below a 2, starting from the top and working your way down, until no such cells remain.

Note that the pattern you end up with will be horizontally symmetric.

Step 2: If needed, solve parities. Based on cells e,f,g,h decide the pattern for cells a,b,c,d:

Use the chart below to find the row for the e,f,g,h cells that correspond to your pattern. Tap the a,b,c,d cells in the corresponding row the number of times specified. Only change the a,b,c,d cells from the upper-left of the puzzle, and not the symmetrical cells on the right (see graph above).

Patterns not listed above should not be possible to achieve.

Step 3: Repeat step 1, and you should end up with a solved board.

Strategy for the Expert puzzle
Step 1:  Click on any cell directly below any cell that is not a 1, starting from the top and working your way down, until no such cells remain.

Note that the pattern you end up with will be horizontally symmetric.

Step 2: If needed, solve parities. Based on cells e,f,g,h, decide the pattern for cells a,b,c,d.

Use the charts below to find the row for the e,f,g,h cells that correspond to your pattern. Tap the a,b,c,d cells in the corresponding row the number of times specified. Only change the a,b,c,d cells from the upper-left of the puzzle, and not the symmetrical cells on the right (see graph above).

Patterns are separated by e=1, 2, 3, 4, 5, or 6 to make them easier to find.

The table on the left represents the numbers on the bottom row of the board, while the table on the right represents the number of times you need to tap a,b,c, & d.

e=1 e=2

e=3

e=4

e=5

e=6

Patterns not listed above should not be possible to achieve.

Step 3: Repeat step 1, and you should end up with a solved 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.