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DaveC426913

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- How many possible shapes can there be, given these parameters?

I'm playing a Steam game called Shapez wherein the goal is to produce and deliver given shapes to the Hub by conveyor belt.

In the screencap you can see resources of

Here's a sample of three different final "products" with multiple quadrants, layers, colours and shapes (all four shapes are at least partially represented here: a disc, star and windmill; a full square is only partially represented):

I was lying awake last night, trying to figure out how many possible products there can be, and I kept getting intuitively wrong numbers.I'll start with the easy one. I'll enumerate

This is a blue windmill, on top of a white disc, on top of a blue disc.Parameters:

So, the number of (symmetrical) products should be 4x7x4 = 112. Is this right? Is this too low?Now we go to asymmetrical products:

Each quadrant of an asymmetrical product can have one quarter of any of the above, so:

112

In the screencap you can see resources of

*discs*and*squares*and well as*green*and*red*, which are to be extracted, chopped up and recombined to form the "product" specified in the Hub.Here's a sample of three different final "products" with multiple quadrants, layers, colours and shapes (all four shapes are at least partially represented here: a disc, star and windmill; a full square is only partially represented):

I was lying awake last night, trying to figure out how many possible products there can be, and I kept getting intuitively wrong numbers.I'll start with the easy one. I'll enumerate

**only products that are fully rotationally symmetrical.**i.e. all four quadrants of the deliverable product are identical. Thus:This is a blue windmill, on top of a white disc, on top of a blue disc.Parameters:

- There are
**four**primary**shape**resources:**square**,**disc**,**star**and**windmill**. - Each shape can have one of
**seven colours**:**R,G,B,C,M,Y and white**. - And there can be up to
**four layers**. (There is always a bottom later;**if**there is a second layer, it is on top of that;**if**there is a third later, it is on top of that, etc. There are no "empty" layers.) *(Size*is not a parameter;*rotational orientation*is not a parameter.)

So, the number of (symmetrical) products should be 4x7x4 = 112. Is this right? Is this too low?Now we go to asymmetrical products:

Each quadrant of an asymmetrical product can have one quarter of any of the above, so:

112

^{4}, or about 157 million, right?I'm just not sure I've enumerated it correctly. I suspect I've done the**layers**wrong in the symmetrical step. It's not just x4, is it? Is it*to the power*of 4?