I have 6 unique modules that need to be placed in a 3x3 grid. Each arrangement should use all 6 modules, leaving exactly 3 positions as empty (voids). I want to know the total number of possible unique combinations that can be generated with this setup, ensuring that each configuration has 6 modules and 3 empty spots. How can I make this ? I tried with two list. Can anyone help with this. I need all the results.
You could do something like this using python to find all permutations:
import itertools
items = ['A', 'B', 'C', 'D', 'E', 'F', 'X', 'X', 'X']
uniqp = set(itertools.permutations(items))
comb = [i for i in uniqp]
a = comb
FYI, there are 60,480.
Hello
quite the same thing using Nautilus plugin and Create Sets, I get old result that I get 30,240 and now 60480. A bit long ~8 minutes for the set.
For 9 elements 362 880 = 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
for 3 elements 2 x 3 = 6
So the result must be like said by @Adam_M 362 880 / 6 = 60,480
See there for others references
If you had 9 different elements, you would have 9! = 362 880 combinations, but 3 elements are the same, so you basically have only a 3!th of the combinations, e.g. division by 6.
362_880 / 6 = 60_480
The error is probably that the component treats every “X” as a unique element, not as the “same”.
I don’t think so, it works here
and now it works !!! There is something strange, but Xreate set is VERY VERY long
or Create Set has a limitation ?
permutations 9 elements LD.gh (294.6 KB)
The permutations function takes a second parameter, enabling one to select N items:
241031_GridPermutationsN_00.gh (11.9 KB)
Also, note that finding the permutations isn’t actually that expensive. It’s outputting all that data that costs, where in this case one should probably wrap the grid cells in a Grasshopper curve type.
I get only 84. Adapted Python code from here:
Combos_2024Oct31a.gh (13.4 KB)
P.S. Added white group as a visual aid:
Combos_2024Oct31bb.gh (19.4 KB) UPDATED!
P.P.S. I noticed that the last two grids (top row) in my visual aid had the same pattern Fortunately it’s a simple off-by-one error, easily fixed. Top row now shows four grids, not five. UPDATED version ‘bb’ above.
Reading that more thoroughly, you probably want to use the combinations
function instead. Which, as @Joseph_Oster points out, yields 84 unique combinations:
241031_GridCombinationsN_00.gh (12.9 KB)
Edit: Made them meshes and slapped them into a grid. I wonder if the same patterns rotated/mirrored would not count as a unique configuration. Either way, fun stuff:
241101_GridCombinationsN_00.gh (15.8 KB)
I made a bitmap with the 60480 permutations I have.
Plugins not mandatory if you have a tool that saves bitmap.
permutations 9 elements LD2.gh (295.9 KB)