Python Program for Triangular Matchstick Number

In this article, we will learn how to calculate the total number of matchsticks required to build a triangular pyramid. Given the number of floors X, we need to find the total matchsticks needed to construct the entire pyramid structure.

Problem statement − We are given a number X which represents the floor of a matchstick pyramid, we need to display the total number of matchsticks required to form a pyramid of matchsticks with X floors.

Understanding the Pattern

In a triangular matchstick pyramid:

• Floor 1 requires 3 matchsticks (forming 1 triangle)
• Floor 2 requires 9 matchsticks (forming 3 triangles)
• Floor 3 requires 18 matchsticks (forming 6 triangles)
• Floor n requires 3n(n+1)/2 matchsticks total

Mathematical Formula

The formula to calculate triangular matchstick numbers is:

Total matchsticks = 3 × n × (n + 1) / 2

Where n is the number of floors in the pyramid.

Example

Let's implement the solution to calculate matchsticks for a 21-floor pyramid ?

# Function to calculate triangular matchstick number
def numberOfSticks(x):
    return (3 * x * (x + 1)) // 2

# Calculate for 21 floors
n = 21
total_sticks = numberOfSticks(n)
print(f"Matchsticks required for {n} floors: {total_sticks}")

Matchsticks required for 21 floors: 693

Step-by-Step Calculation

Let's verify with smaller examples to understand the pattern ?

def numberOfSticks(x):
    return (3 * x * (x + 1)) // 2

# Test with different floor numbers
floors = [1, 2, 3, 4, 5]

print("Floor | Matchsticks")
print("------|------------")
for floor in floors:
    sticks = numberOfSticks(floor)
    print(f"{floor:5} | {sticks:10}")

Floor | Matchsticks
------|------------
    1 |          3
    2 |          9
    3 |         18
    4 |         30
    5 |         45

Alternative Implementation

We can also implement using a loop to see how the pattern builds ?

def numberOfSticksLoop(x):
    total = 0
    for i in range(1, x + 1):
        triangles_in_floor = (i * (i + 1)) // 2
        total += triangles_in_floor * 3
    return total

# Compare both methods
n = 10
method1 = numberOfSticks(n)
method2 = numberOfSticksLoop(n)

print(f"Formula method: {method1}")
print(f"Loop method: {method2}")
print(f"Results match: {method1 == method2}")

Formula method: 165
Loop method: 165
Results match: True

Conclusion

The triangular matchstick number follows the formula 3 × n × (n + 1) / 2. This mathematical approach provides an efficient solution compared to iterative counting, making it ideal for calculating large pyramid structures.