Flipping arrows puzzle

What is flipping arrows?

Flipping arrows is puzzle. The goal is to turn the dices to match the goal you choose.

The goal?

• To have all the top faces white
• To have all the top faces gray
• To have all the top faces white/gray
• To have all the top faces white/gray with the colors in the same direction (difficult)
• To have all the top faces with the same color and the arrow in the same direction (really difficult)

Rules

1. Mix the dices
2. Put them randomly on the board
3. Choose your goal
4. On the top face of a dice have one or two colors and an arrow. You can rotate the dice by 1/4 of turn in the direction of the arrow.
5. Select the dice you want to "flip". The direction of the arrow, indicates the direction of the rotation. Rotate the dice by 1/4 of turn. The dices in the direction of the arrow will also rotate by 1/4 of turn in the same direction of the first dice (no matter the direction of the arrow of theses dices).
6. If the dice is on a side and the arrow face the outside of the board, only this dice rotates.
7. You solved the puzzle when reached the goal set in the step 3

Some examples of movements: 

• If you want to rotate the dice 4. You must rotate dices 4, 5 and 6 of 1/4 of turn in the right direction
• If you want to rotate the dice 5. You must rotate dices 5 and 8 of 1/4 of turn in the bottom direction
• If you want to rotate the dice 1. You must rotate dice 1 of 1/4 of turn in the top direction
• If you want to rotate the dice 6. You must rotate dices 6 and 3 of 1/4 of turn in the top direction. Note that position of dice 9 is unchanged!

How many dices combinations are possible?

• On each face, an arrow can have 4 directions
• A dice have 6 faces
• There is 9 dices on the board

(4*6)^9 = 2 641 807 540 224 combinations

Some combinations are simple to solve and others much more complicated.
The complexity depends on the goal you have chosen.

Portable!

This puzzle is portable. You can keep the current status of the puzzle by putting the lid over the board (see bellow).

When you want to play, remove the lid, return it and stack the board on the lid (see bellow).

How to print?

The 9 dices are printed with 2 colors. Layer 0.2mm. Infill 20%. No brim. No support. 

For best results, change the color at 10.2mm.

For the board and the lid use the same parameters.

Note : I originally publish this design in my Thingiverse page (https://www.thingiverse.com/thing:3077387).

Enjoy :)