Find Out How Many Combinations of n Squares Exist

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SUMMARY

This discussion focuses on calculating the number of unique configurations of n squares and their corresponding perimeters. The complexity increases significantly as n increases, leading to a vast number of combinations. The conversation also explores whether similar calculations can be applied to equilateral triangles. A comparison is drawn to the concept of isomers in chemistry, highlighting the intricate nature of shape combinations.

PREREQUISITES
  • Understanding of combinatorial mathematics
  • Familiarity with geometric shapes and their properties
  • Basic knowledge of perimeter calculations
  • Concept of isomers in chemistry
NEXT STEPS
  • Research combinatorial geometry techniques for calculating configurations
  • Explore algorithms for generating unique shapes from n squares
  • Investigate perimeter calculation methods for complex geometric shapes
  • Learn about the relationship between geometric configurations and chemical isomers
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Mathematicians, educators, geometry enthusiasts, and anyone interested in combinatorial problems and geometric configurations.

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In the picture attached I have tried to list the different shapes you can get when you attach, 1, 2, 3, 4 squares, but, as you can imagine, when n gets bigger the number of combinations gets incredibly large. Is there are way to see how many possible configurations there is for n squares, and the different perimeters of these shapes?
If not is it possible for equilateral triangles?
 

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aaaa202 said:
In the picture attached I have tried to list the different shapes you can get when you attach, 1, 2, 3 squares, but, as you can imagine, when n gets bigger the number of combinations gets incredibly large. Is there are way to see how many possible configurations there is for n squares, and the different perimeters of these shapes?
If not is it possible for equilateral triangles?

Can't see the attachment
EDIT:Now it's there.That is very similar to Isomers of hydrocarbons(Chemistry)
 
Last edited:
now :)
 

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