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I'm struggling to calculate the number of possible combinations this board can have. I'm not sure which calculation to use for this specific problem.

Let's say I have a grid, which is 7x5 in size, so in total there would be 35 blocks. Then I have 35 pyramid blocks which can be placed inside of the grid. Each of these pyramid blocks will be 3 shades of a color. So that's actually then 3 colors per pyramid. So in total, there will only be 7 different colors, but shades of 3 per color. I'm not sure if this will have an impact on the outcome, SO you are looking at 5 pyramid blocks, being the same shades of 3 color. ( Not sure if any of this is making any sense). So you will have :

5 * blue pyramids

5 x peach pyramids

5 x green pyramids

5 x pink pyramids

5 x yellow pyramids

5 x red pyramids

5 x purple pyramids

35 in total.

The blue pyramids will then consist of baby blue, sky blue, midnight blue for example.

So, each of these blocks can be placed inside the grid. The problem is, that every pyramid consists of 3 colors. So, depending on how you place these 35 different pyramids inside of the grid, how many possible combinations can there be?

I was thinking of the formula 35^3 * 7 * 5, but that doesn't sound right.

EDIT:

IF you have a grid 2x2 and 4 pyramids, which consists of 2 main colors, blue and green. 2 blocks will have 2 shades of blue, and 2 block will have 2 shades of green. So that's actually 4 colors in total. And one block can have 4 combinations depending on how you rotate it. So I believe the possible number of combinations for this will then be 256.

rochmit10
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  • Welcome to stackexchange. You are right to think you may not have asked clearly enough. We may be able to help if you [edit] the question to list all the possible combinations for a small version of the problem - perhaps a $2\times 2$ grid, with just two colors of pyramids and two shades of each color. – Ethan Bolker Jun 06 '19 at 14:35
  • Thanks @EthanBolker, I've updated the question. I'm thinking that if you place 2 blue pyramids at the top, en 2 green pyramids at the bottom, and you rotate each block to a different color, then there will be 256 combinations, but what happens when you place a blue & green one at the top, and a blue and green one at the bottom, then the number of combinations can be significantly higher? Then you can also go and place 2 greens at the top, en 2 blues at the bottom and vice versa. This is why I'm struggling because I'm not sure how to calculate the number of possibilities. – rochmit10 Jun 06 '19 at 15:22
  • That is better but still not clear. I don't see any pyramids so can't tell how they are colored and what it means to rotate them. Please [edit] the question to show us some actual examples of that small grid, filled several different ways so we can see what counts as different. You can use letters for colors, and preformatting for arrays, so you don't actually have to upload images. – Ethan Bolker Jun 06 '19 at 16:18

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