Syncro is a beautiful game where you have to unite all the petals in a single flower. In how many moves can you do it?

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Problem statement

Look at the image above. There are four “flowers”, each one with four “petals”. Notice that each of the flowers has one coloured petal. There are also arrows going from one flower to the other: this means that the corresponding shape sends the coloured petals in that direction.

For example, the square makes all coloured petals rotate once in the clockwise direction, or if you take the image above and do “circle + square” then the coloured petals end up like this:

Petal distribution after doing the sequence “circle + square”.

Your objective is to find a sequence of circles and squares that put all coloured petals in a single flower, in the smallest number of steps possible.

Give it some thought...

If you need any clarification whatsoever, feel free to ask in the comment section below.

Syncro

Syncro is a desktop/mobile game developed by some friends of mine, and the objective of the game is the same as that of this problem, except the game itself has several levels.

This game can be played online and there is also an Android app.

If you complete the game, you can even end up in the hall of fame!

Solution

The solution to this problem will be posted here after this problem has been live for 2 weeks. Feel free to email me your solution if you want it featured in the solution page.


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