# Python Program for Maximum Number of 2×2 Squares That Can be Fit Inside a Right Isosceles Triangle

In the previous article, we have discussed Python Program to Find Slope of a Line
Given the base of the isosceles triangle, the task is to find the count of the maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle.

The side of the square must be parallel to the base of the given isosceles triangle.

Examples:

Example1:

Input:

Given base of triangle = 8

Output:

The maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle =  6

Explanation:

Example2:

Input:

Given base of triangle = 6

Output:

The maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle =  3

## Program for Maximum Number of 2×2 Squares That Can be Fit Inside a Right Isosceles Triangle in python:

Below are the ways to find the count of the maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle:

### Method #1: Using Mathematical Formula (Static Input)

Approach:

• Give the base of the triangle as static input and store it in a variable.
• Create a function to say count_Squares() which takes the given base of the isosceles triangle as an argument and returns the count of the maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle.
• Inside the function, subtract 2 from the given base value as it is the extra part.
• Store it in the same variable.
• Divide the given base of the triangle by 2 since each square has a base length of 2.
• Store it in the same variable.
• Calculate the value of gvn_trianglebase * (gvn_trianglebase + 1) / 2 (Mathematical Formula) and store it in another variable.
• Return the above result which is the count of the maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle.
• Pass the given base of the isosceles triangle to the count_Squares() function and print it.
• The Exit of the Program.

Below is the implementation:

# Create a function to say count_Squares() which takes the given base of the isosceles
# triangle as an argument and returns the count of the maximum number of 2*2
# squares required that can be fixed inside the given isosceles triangle.

def count_Squares(gvn_trianglebase):
# Inside the function, subtract 2 from the given base value as it is the extra part.
# Store it in the same variable.

gvn_trianglebase = (gvn_trianglebase - 2)
# Divide the given base of the triangle by 2 since each square has a base length of 2.
# Store it in the same variable.
gvn_trianglebase = gvn_trianglebase // 2
# Calculate the value of gvn_trianglebase * (gvn_trianglebase + 1) / 2
# (Mathematical Formula) and store it in another variable.
rslt = gvn_trianglebase * (gvn_trianglebase + 1) // 2
# Return the above result which is the count of the maximum number of 2*2 squares
# required that can be fixed inside the given isosceles triangle.
return rslt

# Give the base of the triangle as static input and store it in a variable.
gvn_trianglebase = 6
# Pass the given base of the isosceles triangle to the count_Squares() function
# and print it.
print("The maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle = ",
count_Squares(gvn_trianglebase))


Output:

The maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle =  3

### Method #2: Using Mathematical Formula (User Input)

Approach:

• Give the base of the triangle as user input using the int(input()) function and store it in a variable.
• Create a function to say count_Squares() which takes the given base of the isosceles triangle as an argument and returns the count of the maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle.
• Inside the function, subtract 2 from the given base value as it is the extra part.
• Store it in the same variable.
• Divide the given base of the triangle by 2 since each square has a base length of 2.
• Store it in the same variable.
• Calculate the value of gvn_trianglebase * (gvn_trianglebase + 1) / 2 (Mathematical Formula) and store it in another variable.
• Return the above result which is the count of the maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle.
• Pass the given base of the isosceles triangle to the count_Squares() function and print it.
• The Exit of the Program.

Below is the implementation:

# Create a function to say count_Squares() which takes the given base of the isosceles
# triangle as an argument and returns the count of the maximum number of 2*2
# squares required that can be fixed inside the given isosceles triangle.

def count_Squares(gvn_trianglebase):
# Inside the function, subtract 2 from the given base value as it is the extra part.
# Store it in the same variable.

gvn_trianglebase = (gvn_trianglebase - 2)
# Divide the given base of the triangle by 2 since each square has a base length of 2.
# Store it in the same variable.
gvn_trianglebase = gvn_trianglebase // 2
# Calculate the value of gvn_trianglebase * (gvn_trianglebase + 1) / 2
# (Mathematical Formula) and store it in another variable.
rslt = gvn_trianglebase * (gvn_trianglebase + 1) // 2
# Return the above result which is the count of the maximum number of 2*2 squares
# required that can be fixed inside the given isosceles triangle.
return rslt

# Give the base of the triangle as user input using the int(input()) function
# and store it in a variable.
gvn_trianglebase = int(input("Enter some random number = "))
# Pass the given base of the isosceles triangle to the count_Squares() function
# and print it.
print("The maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle = ",
count_Squares(gvn_trianglebase))


Output:

Enter some random number = 8
The maximum number of 2*2 squares required that can be fixed inside the given isosceles triangle = 6

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