Find Out How Many Combinations of n Squares Exist

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In summary, the speaker is discussing the different shapes that can be created by attaching 1, 2, 3, or 4 squares together. They mention that as the number of squares (n) increases, so does the number of possible combinations. They ask if there is a way to calculate the number of possible configurations and the different perimeters of these shapes for n squares, and if this is also possible for equilateral triangles.
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aaaa202
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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)
 
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now :)
 

FAQ: Find Out How Many Combinations of n Squares Exist

What is the purpose of finding out the number of combinations of n squares?

The purpose of finding out the number of combinations of n squares is to understand the total number of possible arrangements or combinations of a given set of squares. This can be useful in various areas of study, such as mathematics, computer science, and statistics.

What is the formula for calculating the number of combinations of n squares?

The formula for calculating the number of combinations of n squares is n! / (r!(n-r)!), where n is the total number of squares and r is the number of squares being chosen for each combination. This formula is known as the combination formula.

How do you apply the formula to find out the number of combinations of n squares?

To apply the formula, simply plug in the values of n and r into the formula and solve for the total number of combinations. For example, if there are 5 squares and you want to know the number of combinations of 3 squares, the calculation would be 5! / (3!(5-3)!) = 10 combinations.

What is the difference between combinations and permutations?

The main difference between combinations and permutations is that combinations focus on the selection of items without considering their order, while permutations take into account the order in which the items are arranged. In other words, combinations are unordered while permutations are ordered.

What are some real-world applications of finding out the number of combinations of n squares?

Some real-world applications of finding out the number of combinations of n squares include predicting outcomes in games of chance, analyzing data in statistics, and solving problems in computer science and mathematics. This concept is also used in various fields such as genetics, chemistry, and economics.

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